{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T21:43:52Z","timestamp":1762033432060},"reference-count":75,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2017,3,28]],"date-time":"2017-03-28T00:00:00Z","timestamp":1490659200000},"content-version":"unspecified","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":[[2017,10]]},"DOI":"10.1007\/s00366-017-0510-5","type":"journal-article","created":{"date-parts":[[2017,3,28]],"date-time":"2017-03-28T17:53:38Z","timestamp":1490723618000},"page":"983-996","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Numerical investigation based on direct meshless local Petrov Galerkin (direct MLPG) method for solving generalized Zakharov system in one and two dimensions and generalized Gross\u2013Pitaevskii equation"],"prefix":"10.1007","volume":"33","author":[{"given":"Mehdi","family":"Dehghan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mostafa","family":"Abbaszadeh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,3,28]]},"reference":[{"key":"510_CR1","doi-asserted-by":"crossref","first-page":"4114","DOI":"10.1016\/j.cnsns.2009.03.001","volume":"14","author":"S Abbasbandy","year":"2009","unstructured":"Abbasbandy S, Babolian E, Ashtiani M (2009) Numerical solution of the generalized Zakharov equation by homotopy analysis method. Commun Nonlinear Sci Numer Simul 14:4114\u20134121","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"510_CR2","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/s004660050346","volume":"22","author":"SN Atluri","year":"1998","unstructured":"Atluri SN, Zhu T (1998) A new meshless local Petrov\u2013Galerkin (MLPG) approach in computational mechanics. Comput Mech 22:117\u2013127","journal-title":"Comput Mech"},{"key":"510_CR3","first-page":"11","volume":"3","author":"SN Atluri","year":"2002","unstructured":"Atluri SN, Shen S (2002) The meshless local Petrov\u2013Galerkin (MLPG) method: a simple and less-costly alternative to the finite element and boundary element methods. Comput Model Eng Sci 3:11\u201351","journal-title":"Comput Model Eng Sci"},{"key":"510_CR4","volume-title":"The meshless method (MLPG) for domain and BIE discretizations","author":"SN Atluri","year":"2004","unstructured":"Atluri SN (2004) The meshless method (MLPG) for domain and BIE discretizations. Tech Science Press, Duluth"},{"key":"510_CR5","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1016\/S0021-9991(03)00102-5","volume":"187","author":"W Bao","year":"2003","unstructured":"Bao W, Jaksch D, Markowich PA (2003) Numerical solution of the Gross\u2013Pitaevskii equation for Bose\u2013Einstein condensation. J Comput Phys 187:318\u2013342","journal-title":"J Comput Phys"},{"key":"510_CR6","doi-asserted-by":"crossref","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 36:1361\u20131369","journal-title":"Eng Anal Bound Elem"},{"key":"510_CR7","doi-asserted-by":"crossref","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 230:7384\u20137399","journal-title":"J Comput Phys"},{"key":"510_CR8","doi-asserted-by":"crossref","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 231:2466\u20132481","journal-title":"J Comput Phys"},{"key":"510_CR9","doi-asserted-by":"crossref","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 229:8281\u20138295","journal-title":"J Comput Phys"},{"key":"510_CR10","first-page":"30","volume":"247","author":"AH Bhrawy","year":"2014","unstructured":"Bhrawy AH (2014) An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system. Appl Math Comput 247:30\u201346","journal-title":"Appl Math Comput"},{"key":"510_CR11","doi-asserted-by":"crossref","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 231:7133\u20137151","journal-title":"J Comput Phys"},{"issue":"1","key":"510_CR12","doi-asserted-by":"crossref","first-page":"1450009","DOI":"10.1142\/S1758825114500094","volume":"6","author":"L Chen","year":"2014","unstructured":"Chen L, Liu C, Ma HP, Cheng YM (2014) An interpolating local Petrov\u2013Galerkin method for potential problems. Int J Appl Mech 6(1):1450009","journal-title":"Int J Appl Mech"},{"issue":"6","key":"510_CR13","doi-asserted-by":"crossref","first-page":"884","DOI":"10.1016\/j.apnum.2007.04.003","volume":"58","author":"R Cheng","year":"2008","unstructured":"Cheng R, Cheng YM (2008) Error estimates for the finite point method. Appl Numer Math 58(6):884\u2013898","journal-title":"Appl Numer Math"},{"issue":"10","key":"510_CR14","doi-asserted-by":"crossref","first-page":"6037","DOI":"10.7498\/aps.57.6037","volume":"57","author":"R Cheng","year":"2008","unstructured":"Cheng R, Cheng YM (2008) Error estimates of element-free Galerkin method for potential problems. Acta Phys Sin 57(10):6037\u20136046","journal-title":"Acta Phys Sin"},{"issue":"9","key":"510_CR15","doi-asserted-by":"crossref","first-page":"090205","DOI":"10.1088\/1674-1056\/21\/9\/090205","volume":"21","author":"YM Cheng","year":"2012","unstructured":"Cheng YM, Li R, Peng M (2012) Complex variable element-free Galerkin method for viscoelasticity problems. Chin Phys B 21(9):090205","journal-title":"Chin Phys B"},{"issue":"4","key":"510_CR16","doi-asserted-by":"crossref","first-page":"1250042","DOI":"10.1142\/S1758825112500421","volume":"4","author":"YM Cheng","year":"2012","unstructured":"Cheng YM, Wang J, Li R (2012) The complex variable element-free Galerkin (CVEFG) method for two-dimensional elastodynamics problems. Int J Appl Mech 4(4):1250042","journal-title":"Int J Appl Mech"},{"issue":"10","key":"510_CR17","doi-asserted-by":"crossref","first-page":"100202","DOI":"10.1088\/1674-1056\/24\/10\/100202","volume":"24","author":"YM Cheng","year":"2015","unstructured":"Cheng YM, Liu C, Bai F, Peng M (2015) Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method. Chin Phys B 24(10):100202","journal-title":"Chin Phys B"},{"key":"510_CR18","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1006\/jcph.2002.6995","volume":"176","author":"SM Cox","year":"2002","unstructured":"Cox SM, Matthews PC (2002) Exponential time differencing for stiff systems. J Comput Phys 176:430\u2013455","journal-title":"J Comput Phys"},{"issue":"2","key":"510_CR19","doi-asserted-by":"crossref","first-page":"597","DOI":"10.7498\/aps.56.597","volume":"56","author":"BD Dai","year":"2007","unstructured":"Dai BD, Cheng YM (2007) Local boundary integral equation method based on radial basis functions for potential problems. Acta Phys Sin 56(2):597\u2013603","journal-title":"Acta Phys Sin"},{"issue":"2","key":"510_CR20","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1142\/S1758825110000561","volume":"2","author":"BD Dai","year":"2010","unstructured":"Dai BD, Cheng YM (2010) An improved local boundary integral equation method for two-dimensional potential problems. Int J Appl Mech 2(2):421\u2013436","journal-title":"Int J Appl Mech"},{"key":"510_CR21","doi-asserted-by":"crossref","unstructured":"Darvishi MT, Arbabi S, Najafi M, Wazwaz AM (2016) Traveling wave solutions of a (2 + 1)-dimensional Zakharov-like equation by the first integral method and the tanh method. Opt Int J Light Electron Opt. Available online 13","DOI":"10.1016\/j.ijleo.2016.04.033"},{"key":"510_CR22","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.cam.2014.02.013","volume":"268","author":"M Dehghan","year":"2014","unstructured":"Dehghan M, Salehi R (2014) A meshless local Petrov\u2013Galerkin method for the time-dependent Maxwell equations. J Comput Appl Math 268:93\u2013110","journal-title":"J Comput Appl Math"},{"key":"510_CR23","doi-asserted-by":"crossref","first-page":"2367","DOI":"10.1016\/j.cam.2011.11.022","volume":"236","author":"M Dehghan","year":"2012","unstructured":"Dehghan M, Salehi R (2012) The numerical solution of the non-linear integro-differential equations based on the meshless method. J Comput Appl Math 236:2367\u20132377","journal-title":"J Comput Appl Math"},{"key":"510_CR24","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1016\/j.cpc.2009.12.010","volume":"181","author":"M Dehghan","year":"2010","unstructured":"Dehghan M, Ghesmati A (2010) Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM). Comput Phys Commun 181:772\u2013786","journal-title":"Comput Phys Commun"},{"key":"510_CR25","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1016\/j.cam.2008.12.011","volume":"230","author":"M Dehghan","year":"2009","unstructured":"Dehghan M, Shokri A (2009) Numerical solution of the nonlinear Klein\u2013Gordon equation using radial basis functions. J Comput Appl Math 230:400\u2013410","journal-title":"J Comput Appl Math"},{"key":"510_CR26","doi-asserted-by":"crossref","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 79:700\u2013715","journal-title":"Math Comput Simul"},{"key":"510_CR27","doi-asserted-by":"crossref","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 43:413\u2013422","journal-title":"Comput Math Appl"},{"key":"510_CR28","doi-asserted-by":"crossref","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"},{"issue":"3","key":"510_CR29","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1007\/BF02731494","volume":"20","author":"EP Gross","year":"1961","unstructured":"Gross EP (1961) Structure of a quantized vortex in boson systems. Il Nuovo Cimento 20(3):454\u2013457","journal-title":"Il Nuovo Cimento"},{"key":"510_CR30","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/S1007-5704(99)90011-4","volume":"4","author":"S Fang","year":"1999","unstructured":"Fang S (1999) A pseudo-spectral approximation for the system of generalized Zakharov equations. Commun Nonlinear Sci Numer Simul 4:227\u2013230","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"510_CR31","doi-asserted-by":"crossref","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 231:4078\u20134095","journal-title":"J Comput Phys"},{"key":"510_CR32","doi-asserted-by":"crossref","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 230:2270\u20132285","journal-title":"J Comput Phys"},{"key":"510_CR33","doi-asserted-by":"crossref","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 65:627\u2013637","journal-title":"Comput Math Appl"},{"key":"510_CR34","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.apnum.2011.08.009","volume":"67","author":"S Ul-Islam","year":"2013","unstructured":"Ul-Islam S, Vertnik R, \u0160arler B (2013) Local radial basis function collocation method along with explicit time stepping for hyperbolic partial differential equations. Appl Numer Math 67:136\u2013151","journal-title":"Appl Numer Math"},{"key":"510_CR35","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1016\/j.apm.2011.07.050","volume":"36","author":"S Ul-Islam","year":"2012","unstructured":"Ul-Islam S, \u0160arler B, Vertnik R, Kosec G (2012) Radial basis function collocation method for the numerical solution of the two-dimensional transient nonlinear coupled Burgers\u2019 equations. Appl Math Model 36:1148\u20131160","journal-title":"Appl Math Model"},{"key":"510_CR36","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.compfluid.2013.10.028","volume":"89","author":"A Javed","year":"2014","unstructured":"Javed A, Djijdeli K, Xing JT (2014) Shape adaptive RBF-FD implicit scheme for incompressible viscous Navier\u2013Stokes equations. Comput Fluids 89:38\u201352","journal-title":"Comput Fluids"},{"key":"510_CR37","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1016\/j.camwa.2006.12.044","volume":"54","author":"M Javidi","year":"2007","unstructured":"Javidi M, Golbabai A (2007) Construction of a solitary wave solution for the generalized Zakharov equation by a variational iteration method. Comput Math Appl 54:1003\u20131009","journal-title":"Comput Math Appl"},{"key":"510_CR38","doi-asserted-by":"crossref","first-page":"1214","DOI":"10.1137\/S1064827502410633","volume":"26","author":"AK Kassam","year":"2005","unstructured":"Kassam AK, Trefethen LN (2005) Fourth-order time-stepping for stiff PDEs. SIAM J Sci Comput 26:1214\u20131233","journal-title":"SIAM J Sci Comput"},{"key":"510_CR39","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.cam.2008.01.017","volume":"223","author":"AQM Khaliq","year":"2009","unstructured":"Khaliq AQM, Martin-Vaquero J, Wade BA, Yousuf M (2009) Smoothing schemes for reaction\u2013diffusion systems with non-smooth data. J Comput Appl Math 223:374\u2013386","journal-title":"J Comput Appl Math"},{"key":"510_CR40","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.jcp.2014.02.025","volume":"267","author":"X Li","year":"2014","unstructured":"Li X, Xiao A (2014) Time-splitting finite difference method with the wavelet-adaptive grids for semiclassical Gross\u2013Pitaevskii equation in super-critical case. J Comput Phys 267:146\u2013161","journal-title":"J Comput Phys"},{"key":"510_CR41","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.apnum.2015.07.006","volume":"99","author":"X Li","year":"2016","unstructured":"Li X (2016) Error estimates for the moving least-square approximation and the element-free Galerkin method in n-dimensional spaces. Appl Numer Math 99:77\u201397","journal-title":"Appl Numer Math"},{"issue":"12","key":"510_CR42","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1016\/j.apnum.2011.08.003","volume":"61","author":"X Li","year":"2011","unstructured":"Li X (2011) Meshless Galerkin algorithms for boundary integral equations with moving least square approximations. Appl Numer Math 61(12):1237\u20131256","journal-title":"Appl Numer Math"},{"issue":"1","key":"510_CR43","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.cam.2008.12.003","volume":"230","author":"X Li","year":"2009","unstructured":"Li X, Zhu J (2009) A Galerkin boundary node method and its convergence analysis. J Comput Appl Math 230(1):314\u2013328","journal-title":"J Comput Appl Math"},{"key":"510_CR44","doi-asserted-by":"crossref","first-page":"510","DOI":"10.4208\/cicp.060414.190914a","volume":"17","author":"X Liang","year":"2015","unstructured":"Liang X, Khaliq AQM, Xing Y (2015) Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schr\u00f6dinger equations. Commun Comput Phys 17:510\u2013541","journal-title":"Commun Comput Phys"},{"key":"510_CR45","first-page":"383","volume":"273","author":"M Ma","year":"2016","unstructured":"Ma M, Dang C, Huang Z (2016) Analytical expressions for dark soliton solution of a Gross\u2013Pitaevskii equation. Appl Math Comput 273:383\u2013389","journal-title":"Appl Math Comput"},{"key":"510_CR46","first-page":"183","volume":"88","author":"A Mazzia","year":"2012","unstructured":"Mazzia A, Pini G, Sartoretto F (2012) Numerical investigation on direct MLPG for 2-D and 3-D potential problems. Comput Model Eng Sci 88:183\u2013209","journal-title":"Comput Model Eng Sci"},{"key":"510_CR47","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1093\/imanum\/drr030","volume":"32","author":"D Mirzaei","year":"2012","unstructured":"Mirzaei D, Schaback R, Dehghan M (2012) On generalized moving least squares and diffuse derivatives. IMA J Numer Anal 32:983\u20131000","journal-title":"IMA J Numer Anal"},{"key":"510_CR48","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.apnum.2013.01.002","volume":"68","author":"D Mirzaei","year":"2013","unstructured":"Mirzaei D, Schaback R (2013) Direct meshless local Petrov-*Galerkin (DMLPG) method: a generalized MLS approximation. Appl Numer Math 68:73\u201382","journal-title":"Appl Numer Math"},{"key":"510_CR49","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s11075-013-9711-1","volume":"65","author":"D Mirzaei","year":"2014","unstructured":"Mirzaei D, Schaback R (2014) Solving heat conduction problems by the direct meshless local Petrov\u2013Galerkin (DMLPG) method. Numer Alg 65:275\u2013291","journal-title":"Numer Alg"},{"key":"510_CR50","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1002\/num.22031","volume":"32","author":"D Mirzaei","year":"2016","unstructured":"Mirzaei D (2016) A greedy meshless local Petrov\u2013Galerkin method based on radial basis functions. Numer Methods Partial Differ Equ 32:847\u2013861","journal-title":"Numer Methods Partial Differ Equ"},{"key":"510_CR51","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.jcp.2013.10.009","volume":"258","author":"H Salman","year":"2014","unstructured":"Salman H (2014) A time-splitting pseudospectral method for the solution of Gross\u2013Pitaevskii equations using spherical harmonics with generalised-Laguerre basis functions. J Comput Phys 258:185\u2013207","journal-title":"J Comput Phys"},{"key":"510_CR52","first-page":"9853","volume":"218","author":"SA Sarra","year":"2012","unstructured":"Sarra SA (2012) A local radial basis function method for advection\u2013diffusion\u2013reaction equations on complexly shaped domains. Appl Math Comput 218:9853\u20139865","journal-title":"Appl Math Comput"},{"key":"510_CR53","doi-asserted-by":"crossref","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":"510_CR54","doi-asserted-by":"crossref","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":"510_CR55","first-page":"8233","volume":"8","author":"F Sartoretto","year":"2014","unstructured":"Sartoretto F, Mazzia A, Pini G (2014) The DMLPG meshless technique for Poisson problems. Appl Math Sci 8:8233\u20138250","journal-title":"Appl Math Sci"},{"key":"510_CR56","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.camwa.2015.11.006","volume":"71","author":"AR Seadawy","year":"2016","unstructured":"Seadawy AR (2016) Three-dimensional nonlinear modified Zakharov\u2013Kuznetsov equation of ion-acoustic waves in a magnetized plasma. Comput Math Appl 71:201\u2013212","journal-title":"Comput Math Appl"},{"key":"510_CR57","doi-asserted-by":"crossref","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\u2013diffusion equations on surfaces. J Sci Comput 63:745\u2013768","journal-title":"J Sci Comput"},{"key":"510_CR58","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1016\/S0045-7825(02)00618-7","volume":"192","author":"C Shu","year":"2003","unstructured":"Shu C, Ding H, Yeo KS (2003) Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 192:941\u2013954","journal-title":"Comput Methods Appl Mech Eng"},{"key":"510_CR59","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1016\/j.enganabound.2006.03.003","volume":"30","author":"J Sladek","year":"2006","unstructured":"Sladek J, Sladek V, Hon YC (2006) Inverse heat conduction problems by meshless local Petrov\u2013Galerkin method. Eng Anal Bound Elem 30:650\u2013661","journal-title":"Eng Anal Bound Elem"},{"key":"510_CR60","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.apnum.2015.08.001","volume":"98","author":"FX Sun","year":"2015","unstructured":"Sun FX, Wang JF, Cheng YM, Huang AX (2015) Error estimates for the interpolating moving least-squares method in n-dimensional space. Appl Numer Math 98:79\u2013105","journal-title":"Appl Numer Math"},{"issue":"2","key":"510_CR61","first-page":"451","volume":"13","author":"LP Pitaevskii","year":"1961","unstructured":"Pitaevskii LP (1961) Vortex lines in an imperfect bose gas. Soviet Phys JETP 13(2):451\u2013454","journal-title":"Soviet Phys JETP"},{"key":"510_CR62","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/j.cma.2014.05.016","volume":"278","author":"A Taleei","year":"2014","unstructured":"Taleei A, Dehghan M (2014) Direct meshless local Petrov\u2013Galerkin method for elliptic interface problems with applications in electrostatic. Comput Methods Appl Mech Eng 278:479\u2013498","journal-title":"Comput Methods Appl Mech Eng"},{"key":"510_CR63","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1002\/num.21935","volume":"31","author":"A Taleei","year":"2015","unstructured":"Taleei A, Dehghan M (2015) An efficient meshfree point collocation moving least squares method to solve the interface problems with nonhomogeneous jump conditions. Numer Methods Partial Differ Eq 31:1031\u20131053","journal-title":"Numer Methods Partial Differ Eq"},{"key":"510_CR64","doi-asserted-by":"crossref","first-page":"6665","DOI":"10.1016\/j.jcp.2012.05.031","volume":"231","author":"M Thalhammer","year":"2012","unstructured":"Thalhammer M, Abhau J (2012) A numerical study of adaptive space and time discretisations for Gross\u2013Pitaevskii equations. J Comput Phys 231:6665\u20136681","journal-title":"J Comput Phys"},{"key":"510_CR65","unstructured":"Tolstykh AI (2000) On using RBFbased differencing formulas for unstructured and mixed structured-unstructured grid calculations. In: Proceedings of the 16th IMACS World Congress, Lausanne"},{"key":"510_CR66","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/s00466-003-0501-9","volume":"33","author":"AI Tolstykh","year":"2003","unstructured":"Tolstykh AI, Shirobokov DA (2003) On using radial basis functions in a finite difference mode with applications to elasticity problems. Comput Mech 33:68\u201379","journal-title":"Comput Mech"},{"key":"510_CR67","first-page":"321","volume":"245","author":"JF Wang","year":"2014","unstructured":"Wang JF, Sun FX, Cheng YM, Huang AX (2014) Error estimates for the interpolating moving least-squares method. Appl Math Comput 245:321\u2013342","journal-title":"Appl Math Comput"},{"key":"510_CR68","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/j.enganabound.2014.10.001","volume":"50","author":"B Wang","year":"2015","unstructured":"Wang B (2015) A local meshless method based on moving least squares and local radial basis functions. Eng Anal Bound Elem 50:395\u2013401","journal-title":"Eng Anal Bound Elem"},{"key":"510_CR69","doi-asserted-by":"crossref","first-page":"5139","DOI":"10.1016\/j.apm.2015.12.035","volume":"40","author":"H Wang","year":"2016","unstructured":"Wang H, Yan G (2016) Lattice Boltzmann model for the interaction of (2 + 1)-dimensional solitons in generalized Gross-Pitaevskii equation. Appl Math Model 40:5139\u20135152","journal-title":"Appl Math Model"},{"key":"510_CR70","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1016\/j.cnsns.2006.10.007","volume":"13","author":"AM Wazwaz","year":"2008","unstructured":"Wazwaz AM (2008) The extended tanh method for the Zakharov\u2013Kuznetsov (ZK) equation, the modified ZK equation, and its generalized forms. Commun Nonlinear Sci Numer Simul 13:1039\u20131047","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"510_CR71","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/j.cnsns.2004.03.001","volume":"10","author":"AM Wazwaz","year":"2005","unstructured":"Wazwaz AM (2005) Exact solutions with solitons and periodic structures for the Zakharov\u2013Kuznetsov (ZK) equation and its modified form. Commun Nonlinear Sci Numer Simul 10:597\u2013606","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"510_CR72","first-page":"577","volume":"161","author":"AM Wazwaz","year":"2005","unstructured":"Wazwaz AM (2005) Nonlinear dispersive special type of the Zakharov\u2013Kuznetsov equation ZK(n, n) with compact and noncompact structures. Appl Math Comput 161:577\u2013590","journal-title":"Appl Math Comput"},{"key":"510_CR73","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1016\/j.jcp.2009.10.029","volume":"229","author":"Y Xia","year":"2010","unstructured":"Xia Y, Xu Y, Shu CW (2010) Local discontinuous Galerkin methods for the generalized Zakharov system. J Comput Phys 229:1238\u20131259","journal-title":"J Comput Phys"},{"key":"510_CR74","doi-asserted-by":"crossref","first-page":"677","DOI":"10.3934\/dcdsb.2007.8.677","volume":"8","author":"Y Xia","year":"2007","unstructured":"Xia Y, Xu Y, Shu CW (2007) Efficient time discretization for local discontinuous Galerkin methods. Discret Contin Dyn S Ser B 8:677\u2013693","journal-title":"Discret Contin Dyn S Ser B"},{"key":"510_CR75","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1016\/j.camwa.2006.12.048","volume":"54","author":"J Zhang","year":"2007","unstructured":"Zhang J (2007) Variational approach to solitary wave solution of the generalized Zakharov equation. Comput Math Appl 54:1043\u20131046","journal-title":"Comput Math Appl"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00366-017-0510-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-017-0510-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-017-0510-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,27]],"date-time":"2022-07-27T00:06:56Z","timestamp":1658880416000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00366-017-0510-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,28]]},"references-count":75,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,10]]}},"alternative-id":["510"],"URL":"https:\/\/doi.org\/10.1007\/s00366-017-0510-5","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,28]]}}}