{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:46:51Z","timestamp":1760784411445},"reference-count":77,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,2,6]],"date-time":"2018-02-06T00:00:00Z","timestamp":1517875200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2019,1]]},"DOI":"10.1007\/s00366-018-0585-7","type":"journal-article","created":{"date-parts":[[2018,2,6]],"date-time":"2018-02-06T02:06:37Z","timestamp":1517882797000},"page":"87-100","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Numerical solution of a time-fractional PDE in the electroanalytical chemistry by a local meshless method"],"prefix":"10.1007","volume":"35","author":[{"given":"Gholamreza","family":"Karamali","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mehdi","family":"Dehghan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mostafa","family":"Abbaszadeh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,2,6]]},"reference":[{"key":"585_CR1","doi-asserted-by":"publisher","first-page":"2212","DOI":"10.1016\/j.camwa.2007.11.012","volume":"55","author":"B Baeumer","year":"2008","unstructured":"Baeumer B, Kovacs M, Meerschaert MM (2008) Numerical solutions for fractional reaction-diffusion equations. Comput Math Appl 55:2212\u20132226","journal-title":"Comput Math Appl"},{"key":"585_CR2","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1122\/1.549724","volume":"27","author":"R Bagley","year":"1983","unstructured":"Bagley R, Torvik P (1983) A theoretical basis for the application of fractional calculus to viscoelasticity. J Rheol 27:201\u2013210","journal-title":"J Rheol"},{"issue":"22","key":"585_CR3","doi-asserted-by":"publisher","first-page":"8281","DOI":"10.1016\/j.jcp.2010.07.008","volume":"229","author":"V Bayona","year":"2010","unstructured":"Bayona V, Moscoso M, Carretero M, Kindelan M (2010) RBF-FD formulas and convergence properties. J Comput Phys 229(22):8281\u20138295","journal-title":"J Comput Phys"},{"issue":"19","key":"585_CR4","doi-asserted-by":"publisher","first-page":"7384","DOI":"10.1016\/j.jcp.2011.06.005","volume":"230","author":"V Bayona","year":"2011","unstructured":"Bayona V, Moscoso M, Kindelan M (2011) Optimal constant shape parameter for multiquadric based RBF-FD method. J Comput Phys 230(19):7384\u20137399","journal-title":"J Comput Phys"},{"issue":"9","key":"585_CR5","doi-asserted-by":"publisher","first-page":"1361","DOI":"10.1016\/j.enganabound.2012.03.010","volume":"36","author":"V Bayona","year":"2012","unstructured":"Bayona V, Moscoso M, Kindelan M (2012) Gaussian RBF-FD weights and its corresponding local truncation errors. Eng Anal Bound Elem 36(9):1361\u20131369","journal-title":"Eng Anal Bound Elem"},{"issue":"6","key":"585_CR6","doi-asserted-by":"publisher","first-page":"2466","DOI":"10.1016\/j.jcp.2011.11.036","volume":"231","author":"V Bayona","year":"2012","unstructured":"Bayona V, Moscoso M, Kindelan M (2012) Optimal variable shape parameter for multiquadric based RBF-FD method. J Comput Phys 231(6):2466\u20132481","journal-title":"J Comput Phys"},{"issue":"1","key":"585_CR7","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/0021-9991(72)90089-7","volume":"10","author":"R Bellman","year":"1972","unstructured":"Bellman R, Kashef B, Casti J (1972) Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J Comput Phys 10(1):40\u201352","journal-title":"J Comput Phys"},{"issue":"21","key":"585_CR8","doi-asserted-by":"publisher","first-page":"7133","DOI":"10.1016\/j.jcp.2012.06.030","volume":"231","author":"EF Bollig","year":"2012","unstructured":"Bollig EF, Flyer N, Erlebacher G (2012) Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs. J Comput Phys 231(21):7133\u20137151","journal-title":"J Comput Phys"},{"key":"585_CR9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511543241","volume-title":"Radial basis functions: theory and implementations","author":"MD Buhmann","year":"2003","unstructured":"Buhmann MD (2003) Radial basis functions: theory and implementations, vol 12. Cambridge University Press, Cambridge"},{"issue":"2","key":"585_CR10","doi-asserted-by":"publisher","first-page":"886","DOI":"10.1016\/j.jcp.2007.05.012","volume":"227","author":"CM Chen","year":"2007","unstructured":"Chen CM, Liu F, Turner I, Anh V (2007) A Fourier method for the fractional diffusion equation describing sub-diffusion. J Comput Phys 227(2):886\u2013897","journal-title":"J Comput Phys"},{"key":"585_CR11","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1016\/j.enganabound.2011.07.008","volume":"36","author":"AHD Cheng","year":"2012","unstructured":"Cheng AHD (2012) Multiquadric and its shape parameter-A numerical investigation of error estimate, condition number, and round-of-error by arbitrary precision computation. Eng Anal Bound Elem 36:220\u2013239","journal-title":"Eng Anal Bound Elem"},{"issue":"1","key":"585_CR12","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1080\/00207160500069847","volume":"83","author":"M Dehghan","year":"2006","unstructured":"Dehghan M (2006) Solution of a partial integro-differential equation arising from viscoelasticity. Int J Comput Math 83(1):123\u2013129","journal-title":"Int J Comput Math"},{"issue":"2","key":"585_CR13","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1002\/num.20460","volume":"26","author":"M Dehghan","year":"2010","unstructured":"Dehghan M, Manafian J, Saadatmandi A (2010) Solving nonlinear fractional partial differential equations using the homotopy analysis method. Numer Methods Partial Differ Equations 26(2):448\u2013479","journal-title":"Numer Methods Partial Differ Equations"},{"issue":"18","key":"585_CR14","doi-asserted-by":"publisher","first-page":"8578","DOI":"10.1016\/j.apm.2013.03.054","volume":"37","author":"M Dehghan","year":"2013","unstructured":"Dehghan M, Nikpour A (2013) Numerical solution of the system of second-order boundary value problems using the local radial basis functions based differential quadrature collocation method. Appl Math Model 37(18):8578\u20138599","journal-title":"Appl Math Model"},{"issue":"9","key":"585_CR15","doi-asserted-by":"publisher","first-page":"2145","DOI":"10.1016\/j.cpc.2013.04.010","volume":"184","author":"M Dehghan","year":"2013","unstructured":"Dehghan M, Nikpour A (2013) The solitary wave solution of coupled Klein\u2013Gordon\u2013Zakharov equations via two different numerical methods. Comput Phys Commun 184(9):2145\u20132158","journal-title":"Comput Phys Commun"},{"key":"585_CR16","doi-asserted-by":"publisher","unstructured":"Dehghan M, Abbaszadeh M (2017) An upwind local radial basis functions-differential quadrature (RBF-DQ) method with proper orthogonal decomposition (POD) approach for solving compressible Euler equation. Eng Anal Bound Elem. https:\/\/doi.org\/10.1016\/j.enganabound.2017.10.004 (in press)","DOI":"10.1016\/j.enganabound.2017.10.004"},{"key":"585_CR17","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.enganabound.2014.10.008","volume":"51","author":"M Dehghan","year":"2015","unstructured":"Dehghan M, Mohammadi V (2015) The numerical solution of Cahn\u2013Hilliard (CH) equation in one, two and three-dimensions via globally radial basis functions (GRBFs) and RBFs-differential quadrature (RBFs-DQ) methods. Eng Anal Bound Elem 51:74\u2013100","journal-title":"Eng Anal Bound Elem"},{"issue":"3","key":"585_CR18","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1016\/j.matcom.2008.04.018","volume":"79","author":"M Dehghan","year":"2008","unstructured":"Dehghan M, Shokri A (2008) A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions. Math Comput Simul 79(3):700\u2013715","journal-title":"Math Comput Simul"},{"issue":"1","key":"585_CR19","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.matcom.2005.10.001","volume":"71","author":"M Dehghan","year":"2006","unstructured":"Dehghan M (2006) Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices. Math Comput Simul 71(1):16\u201330","journal-title":"Math Comput Simul"},{"issue":"3","key":"585_CR20","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/S0898-1221(01)00295-4","volume":"43","author":"TA Driscoll","year":"2002","unstructured":"Driscoll TA, Fornberg B (2002) Interpolation in the limit of increasingly flat radial basis functions. Comput Math Appl 43(3):413\u2013422","journal-title":"Comput Math Appl"},{"key":"585_CR21","doi-asserted-by":"publisher","DOI":"10.1142\/6437","volume-title":"Meshfree approximation methods with MATLAB","author":"GE Fasshauer","year":"2007","unstructured":"Fasshauer GE (2007) Meshfree approximation methods with MATLAB. World Scientific, Singapore"},{"issue":"11","key":"585_CR22","doi-asserted-by":"publisher","first-page":"4078","DOI":"10.1016\/j.jcp.2012.01.028","volume":"231","author":"N Flyer","year":"2012","unstructured":"Flyer N, Lehto E, Blaise S, Wright GB, St-Cyr A (2012) A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere. J Comput Phys 231(11):4078\u20134095","journal-title":"J Comput Phys"},{"issue":"6","key":"585_CR23","doi-asserted-by":"publisher","first-page":"2270","DOI":"10.1016\/j.jcp.2010.12.014","volume":"230","author":"B Fornberg","year":"2011","unstructured":"Fornberg B, Lehto E (2011) Stabilization of RBF-generated finite difference methods for convective PDEs. J Comput Phys 230(6):2270\u20132285","journal-title":"J Comput Phys"},{"issue":"4","key":"585_CR24","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1016\/j.camwa.2012.11.006","volume":"65","author":"B Fornberg","year":"2013","unstructured":"Fornberg B, Lehto E, Powell C (2013) Stable calculation of Gaussian-based RBF-FD stencils. Comput Math Appl 65(4):627\u2013637","journal-title":"Comput Math Appl"},{"key":"585_CR25","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1016\/j.jcp.2010.10.007","volume":"230","author":"GH Gao","year":"2011","unstructured":"Gao GH, Sun ZZ (2011) Compact finite difference scheme for the fractional sub-diffusion equations. J Comput Phys 230:586\u2013595","journal-title":"J Comput Phys"},{"key":"585_CR26","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/j.enganabound.2014.10.018","volume":"52","author":"P Gonzalez-Rodriguez","year":"2015","unstructured":"Gonzalez-Rodriguez P, Bayona V, Moscoso M, Kindelan M (2015) Laurent series based RBF-FD method to avoid ill-conditioning. Eng Anal Bound Elem 52:24\u201331","journal-title":"Eng Anal Bound Elem"},{"key":"585_CR27","doi-asserted-by":"publisher","first-page":"2043","DOI":"10.1021\/ac60334a027","volume":"45","author":"M Goto","year":"1973","unstructured":"Goto M, Oldham KB (1973) Semiintegral electroanalysis: shapes of neopolarograrns. Anal Chem 45:2043\u20132050","journal-title":"Anal Chem"},{"key":"585_CR28","doi-asserted-by":"publisher","first-page":"1522","DOI":"10.1021\/ac60347a058","volume":"46","author":"M Goto","year":"1973","unstructured":"Goto M, Oldham KB (1973) Semiintegral electroanalysis: studies on the neopolarograrns plateau. Anal Chem 46:1522\u20131530","journal-title":"Anal Chem"},{"key":"585_CR29","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1016\/S0022-0728(75)80237-3","volume":"61","author":"M Goto","year":"1975","unstructured":"Goto M, Ishii D (1975) Semidifferential elertroanalysis. J Electroanal Chem Interfacial Electrochem 61:361\u2013365","journal-title":"J Electroanal Chem Interfacial Electrochem"},{"key":"585_CR30","first-page":"1121","volume":"44","author":"M Grenness","year":"1972","unstructured":"Grenness M, Oldham KB (1972) Semiintegral electroanalysis: theory and verification. Anal Cllem 44:1121\u20131129","journal-title":"Anal Cllem"},{"key":"585_CR31","doi-asserted-by":"publisher","first-page":"1673","DOI":"10.1016\/j.cma.2006.09.017","volume":"196","author":"YT Gu","year":"2007","unstructured":"Gu YT, Wang QX, Lam KY (2007) A meshless local Kriging method for large deformation analyses. Comput Methods Appl Mech Eng 196:1673\u20131684","journal-title":"Comput Methods Appl Mech Eng"},{"key":"585_CR32","doi-asserted-by":"publisher","first-page":"5515","DOI":"10.1016\/S0045-7825(01)00180-3","volume":"190","author":"YT Gu","year":"2001","unstructured":"Gu YT, Liu GR (2001) A local point interpolation method for static and dynamic analysis of thin beams. Comput Methods Appl Mech Eng 190:5515\u20135528","journal-title":"Comput Methods Appl Mech Eng"},{"key":"585_CR33","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/j.engfracmech.2010.10.014","volume":"78","author":"YT Gu","year":"2011","unstructured":"Gu YT, Wang W, Zhang LC, Feng XQ (2011) An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields. Eng Fract Mech 78:175\u2013190","journal-title":"Eng Fract Mech"},{"key":"585_CR34","first-page":"1705","volume":"76","author":"RL Hardy","year":"1971","unstructured":"Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76:1705\u20131915","journal-title":"J Geophys Res"},{"key":"585_CR35","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1016\/S0378-4371(99)00469-0","volume":"276","author":"BI Henry","year":"2000","unstructured":"Henry BI, Wearne SL (2000) Fractional reaction-diffusion. Phys A 276:448\u2013455","journal-title":"Phys A"},{"key":"585_CR36","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/0898-1221(90)90270-T","volume":"19","author":"EJ Kansa","year":"1990","unstructured":"Kansa EJ (1990) Multiquadrics A scattered data approximation scheme with applications to computational fluid-dynamics I. Comput Math Appl 19:127\u2013145","journal-title":"Comput Math Appl"},{"key":"585_CR37","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/0898-1221(90)90271-K","volume":"19","author":"EJ Kansa","year":"1990","unstructured":"Kansa EJ (1990) Multiquadrics A scattered data approximation scheme with applications to computational fluid dynamics\u2014II. Comput Math Appl 19:147\u2013161","journal-title":"Comput Math Appl"},{"key":"585_CR38","doi-asserted-by":"publisher","first-page":"940","DOI":"10.1016\/j.enganabound.2009.02.008","volume":"33","author":"EJ Kansa","year":"2009","unstructured":"Kansa EJ, Aldredge RC, Ling L (2009) Numerical simulation of two-dimensional combustion using mesh-free methods. Eng Anal Bound Elem 33:940\u2013950","journal-title":"Eng Anal Bound Elem"},{"key":"585_CR39","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/0022-0728(92)80065-C","volume":"322","author":"AM Keightley","year":"1992","unstructured":"Keightley AM, Myland JC, Oldham KB, Symons PG (1992) Reversiblc cyclic volammetry in the presense of product. J Electronal Chem 322:25\u201354","journal-title":"J Electronal Chem"},{"issue":"5","key":"585_CR40","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1016\/j.enganabound.2011.11.009","volume":"36","author":"SS Kutanaei","year":"2012","unstructured":"Kutanaei SS, Roshan N, Vosoughi A, Saghafi S, Barari A, Soleimani S (2012) Numerical solution of Stokes flow in a circular cavity using mesh-free local RBF-DQ. Eng Anal Bound Elem 36(5):633\u2013638","journal-title":"Eng Anal Bound Elem"},{"key":"585_CR41","doi-asserted-by":"publisher","unstructured":"Li CP, Ding H (2014) Higher order finite difference method for the reaction and anomalous-diffusion equation. Appl Math Model. https:\/\/doi.org\/10.1016\/j.apm.2013.12.002 (in press)","DOI":"10.1016\/j.apm.2013.12.002"},{"key":"585_CR42","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/j.jcp.2012.11.005","volume":"236","author":"L Li","year":"2013","unstructured":"Li L, Xu D (2013) Alternating direction implicit-Euler method for the two-dimensional fractional evolution equation. J Comput Phys 236:157\u2013168","journal-title":"J Comput Phys"},{"key":"585_CR43","volume-title":"An introduction to meshfree methods and their programming","author":"GR Liu","year":"2005","unstructured":"Liu GR, Gu YT (2005) An introduction to meshfree methods and their programming. Springer Dordrecht, Berlin, Heidelberg, New York"},{"key":"585_CR44","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1137\/0727002","volume":"27","author":"JC Lopez-Marcos","year":"1990","unstructured":"Lopez-Marcos JC (1990) A difference scheme for a nonlinear partial integro-differential equation. SIAM J Numer Anal 27:20\u201331","journal-title":"SIAM J Numer Anal"},{"key":"585_CR45","doi-asserted-by":"publisher","first-page":"R161","DOI":"10.1088\/0305-4470\/37\/31\/R01","volume":"37","author":"R Metzler","year":"2004","unstructured":"Metzler R, Klafter J (2004) The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J Phys A 37:R161\u2013208","journal-title":"J Phys A"},{"key":"585_CR46","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/BF02832308","volume":"24","author":"S Momani","year":"2007","unstructured":"Momani S, Odibat ZM (2007) Fractional green function for linear time-fractional inhomogeneous partial differential equations in fluid mechanics. J Appl Math Comput 24:167\u2013178","journal-title":"J Appl Math Comput"},{"key":"585_CR47","doi-asserted-by":"publisher","first-page":"2013","DOI":"10.1016\/j.matcom.2008.08.003","volume":"79","author":"ZM Odibat","year":"2009","unstructured":"Odibat ZM (2009) Computational algorithms for computing the fractional derivatives of functions. Math Comput Simul 79:2013\u20132020","journal-title":"Math Comput Simul"},{"key":"585_CR48","volume-title":"The fractional calculus: theory and application of differentiation and integration to arbitrary order","author":"KB Oldham","year":"1974","unstructured":"Oldham KB, Spanier J (1974) The fractional calculus: theory and application of differentiation and integration to arbitrary order. Academic Press, New York"},{"key":"585_CR49","volume-title":"The fractional calculus","author":"KB Oldham","year":"1974","unstructured":"Oldham KB, Spanier J (1974) The fractional calculus. Academic Press, New York, London"},{"key":"585_CR50","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1021\/ac60309a028","volume":"44","author":"KR Oldham","year":"1972","unstructured":"Oldham KR (1972) A signal-independent electroanalytical method. Anal Chenl 44:196\u2013198","journal-title":"Anal Chenl"},{"key":"585_CR51","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1016\/S0022-0728(76)80323-3","volume":"72","author":"KB Oldham","year":"1976","unstructured":"Oldham KB (1976) Semiintegration of cyclic voltammograms. J Electronnal Chem 72:371\u2013378","journal-title":"J Electronnal Chem"},{"key":"585_CR52","doi-asserted-by":"publisher","first-page":"1068","DOI":"10.1007\/BF01041448","volume":"21","author":"KB Oldham","year":"1991","unstructured":"Oldham KB (1991) Interrelation of current and concentration at electrodes. I. Appl Electrochem 21:1068\u20131072","journal-title":"Appl Electrochem"},{"key":"585_CR53","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1016\/S0022-0728(70)80316-3","volume":"26","author":"KB Oldham","year":"1970","unstructured":"Oldham KB, Spanier J (1970) The replacement of Fick\u2019s law by a formulation involving semidifferentiation. J Electroanal Chem Interfacial Electrochem 26:331\u2013341","journal-title":"J Electroanal Chem Interfacial Electrochem"},{"key":"585_CR54","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1023\/A:1018975909870","volume":"11","author":"S Rippa","year":"1999","unstructured":"Rippa S (1999) An algorithm for selecting a good value for the parameter $$c$$ c in radial basis function interpolation. Adv Comput Math 11:193\u2013210","journal-title":"Adv Comput Math"},{"key":"585_CR55","volume-title":"Fractional differential equations","author":"I Podulbny","year":"1999","unstructured":"Podulbny I (1999) Fractional differential equations. Academic Press, New York"},{"issue":"3","key":"585_CR56","doi-asserted-by":"publisher","first-page":"1326","DOI":"10.1016\/j.camwa.2009.07.006","volume":"59","author":"A Saadatmandi","year":"2010","unstructured":"Saadatmandi A, Dehghan M (2010) A new operational matrix for solving fractional-order differential equations. Comput Math Appl 59(3):1326\u20131336","journal-title":"Comput Math Appl"},{"issue":"19","key":"585_CR57","first-page":"9853","volume":"218","author":"SA Sarra","year":"2012","unstructured":"Sarra SA (2012) A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains. Appl Math Comput 218(19):9853\u20139865","journal-title":"Appl Math Comput"},{"key":"585_CR58","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.enganabound.2014.04.019","volume":"44","author":"SA Sarra","year":"2014","unstructured":"Sarra SA (2014) Regularized symmetric positive definite matrix factorizations for linear systems arising from RBF interpolation and differentiation. Eng Anal Bound Elem 44:76\u201386","journal-title":"Eng Anal Bound Elem"},{"key":"585_CR59","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.enganabound.2010.05.011","volume":"35","author":"SA Sarra","year":"2011","unstructured":"Sarra SA (2011) Radial basis function approximation methods with extended precision floating point arithmetic. Eng Anal Bound Elem 35:68\u201376","journal-title":"Eng Anal Bound Elem"},{"key":"585_CR60","first-page":"333","volume":"34","author":"A Shokri","year":"2012","unstructured":"Shokri A, Dehghan M (2012) Meshless method using radial basis functions for the numerical solution of two-dimensional complex Ginzburg\u2013Landau equation. Comput Model Eng Sci 34:333\u2013358","journal-title":"Comput Model Eng Sci"},{"issue":"3","key":"585_CR61","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1007\/s10915-014-9914-1","volume":"63","author":"V Shankar","year":"2015","unstructured":"Shankar V, Wright GB, Kirby RM, Fogelson AL (2015) A radial basis function (RBF)-finite difference (FD) method for diffusion and reaction-diffusion equations on surfaces. J Sci Comput 63(3):745\u2013768","journal-title":"J Sci Comput"},{"issue":"7","key":"585_CR62","doi-asserted-by":"publisher","first-page":"941","DOI":"10.1016\/S0045-7825(02)00618-7","volume":"192","author":"C Shu","year":"2003","unstructured":"Shu C, Ding H, Yeo K (2003) Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier\u2013Stokes equations. Comput Methods Appl Mech Eng 192(7):941\u2013954","journal-title":"Comput Methods Appl Mech Eng"},{"key":"585_CR63","volume-title":"Differential quadrature and its application in engineering","author":"C Shu","year":"2012","unstructured":"Shu C (2012) Differential quadrature and its application in engineering. Springer, New York"},{"issue":"10","key":"585_CR64","doi-asserted-by":"publisher","first-page":"1217","DOI":"10.1016\/j.enganabound.2003.02.001","volume":"28","author":"C Shu","year":"2004","unstructured":"Shu C, Ding H, Yeo K (2004) Solution of partial differential equations by a global radial basis function-based differential quadrature method. Eng Anal Bound Elem 28(10):1217\u20131226","journal-title":"Eng Anal Bound Elem"},{"key":"585_CR65","doi-asserted-by":"publisher","first-page":"468","DOI":"10.1016\/0021-9991(84)90128-1","volume":"54","author":"AT Patera","year":"1984","unstructured":"Patera AT (1984) A spectral element method for fluid dynamics: laminar flow in a channel expansion. J Comput Phys 54:468\u2013488","journal-title":"J Comput Phys"},{"key":"585_CR66","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.enganabound.2015.06.009","volume":"61","author":"H Roohani Ghehsareh","year":"2015","unstructured":"Roohani Ghehsareh H, Bateni SH, Zaghian A (2015) A meshfree method based on the radial basis functions for solution of two-dimensional fractional evolution equation. Eng Anal Bound Elem 61:52\u201360","journal-title":"Eng Anal Bound Elem"},{"key":"585_CR67","doi-asserted-by":"publisher","first-page":"031102","DOI":"10.1103\/PhysRevE.73.031102","volume":"73","author":"IM Sokolov","year":"2006","unstructured":"Sokolov IM, Schmidt MGW, Sagu\u00e9s F (2006) On reaction-subdiffusion equations. Phys Rev E 73:031102","journal-title":"Phys Rev E"},{"issue":"1","key":"585_CR68","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1007\/s00466-003-0501-9","volume":"33","author":"A Tolstykh","year":"2003","unstructured":"Tolstykh A, Shirobokov D (2003) On using radial basis functions in a finite difference mode with applications to elasticity problems. Comput Mech 33(1):68\u201379","journal-title":"Comput Mech"},{"key":"585_CR69","unstructured":"Tolstykh AI (2000) On using RBF-based differencing formulas for unstructured and mixed structured-unstructured grid calculations. In: Proceedings of the 16th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation. Lausanne, p 6"},{"key":"585_CR70","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.compositesb.2016.05.049","volume":"99","author":"F Tornabene","year":"2016","unstructured":"Tornabene F, Fantuzzi N, Bacciocchi M, Neves AM, Ferreira AJ (2016) MLSDQ based on RBFs for the free vibrations of laminated composite doubly-curved shells. Compos B Eng 99:30\u201347","journal-title":"Compos B Eng"},{"key":"585_CR71","volume-title":"Numerical approximation of partial differential equations","author":"A Quarteroni","year":"1997","unstructured":"Quarteroni A, Valli A (1997) Numerical approximation of partial differential equations. Springer, New York"},{"key":"585_CR72","unstructured":"Wendland H (2005) Scattered data approximation. In: Cambridge monograph on applied and computational mathematics. Cambridge University Press, Cambridge"},{"key":"585_CR73","doi-asserted-by":"publisher","first-page":"2782","DOI":"10.1063\/1.527251","volume":"27","author":"W Wess","year":"1996","unstructured":"Wess W (1996) The fractional diffusion equation. J Math Phys 27:2782\u20132785","journal-title":"J Math Phys"},{"key":"585_CR74","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1016\/j.jcp.2005.12.006","volume":"216","author":"SB Yuste","year":"2006","unstructured":"Yuste SB (2006) Weighted average finite difference methods for fractional diffusion equations. J Comput Phys 216:264\u2013274","journal-title":"J Comput Phys"},{"key":"585_CR75","doi-asserted-by":"publisher","first-page":"036126","DOI":"10.1103\/PhysRevE.69.036126","volume":"69","author":"SB Yuste","year":"2004","unstructured":"Yuste SB, Acedo L, Lindenberg K (2004) Reaction front in an $$A+B \\rightarrow C$$ A + B \u2192 C reaction-subdiffusion process. Phys Rev E 69:036126","journal-title":"Phys Rev E"},{"key":"585_CR76","doi-asserted-by":"publisher","first-page":"496","DOI":"10.4208\/aamm.10-m1210","volume":"4","author":"N Zhang","year":"2012","unstructured":"Zhang N, Deng W, Wu Y (2012) Finite difference\/element method for a two-dimensional modified fractional diffusion equation. Adv Appl Math Mech 4:496\u2013518","journal-title":"Adv Appl Math Mech"},{"key":"585_CR77","first-page":"1","volume":"74","author":"P Zhuang","year":"2005","unstructured":"Zhuang P, Liu F, Anh V, Turner I (2005) Stability and convergence of an implicit numerical method for the nonlinear fractional reaction-subdiffusion process. IMA J Appl Math 74:1\u201322","journal-title":"IMA J Appl Math"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00366-018-0585-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-018-0585-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-018-0585-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,27]],"date-time":"2020-10-27T14:50:21Z","timestamp":1603810221000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00366-018-0585-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,6]]},"references-count":77,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["585"],"URL":"https:\/\/doi.org\/10.1007\/s00366-018-0585-7","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,6]]},"assertion":[{"value":"23 June 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 January 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 February 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}