{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:49:26Z","timestamp":1759837766908,"version":"3.40.3"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319202389"},{"type":"electronic","value":"9783319202396"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-20239-6_33","type":"book-chapter","created":{"date-parts":[[2015,6,16]],"date-time":"2015-06-16T06:20:53Z","timestamp":1434435653000},"page":"307-314","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Finite Difference Method for Two-Sided Space-Fractional Partial Differential Equations"],"prefix":"10.1007","author":[{"given":"Kamal","family":"Pal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fang","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yubin","family":"Yan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Graham","family":"Roberts","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,6,17]]},"reference":[{"key":"33_CR1","doi-asserted-by":"publisher","first-page":"1225","DOI":"10.4134\/BKMS.2010.47.6.1225","volume":"47","author":"HW Choi","year":"2010","unstructured":"Choi, H.W., Chung, S.K., Lee, Y.J.: Numerical solutions for space fractional dispersion equations with nonlinear source terms. Bull. Korean Math. Soc. 47, 1225\u20131234 (2010)","journal-title":"Bull. Korean Math. Soc."},{"key":"33_CR2","first-page":"1","volume":"5","author":"K Diethelm","year":"1997","unstructured":"Diethelm, K.: An algorithm for the numerical solution of differential equations of fractional order. Electron. Trans. Numer. Anal. 5, 1\u20136 (1997)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"33_CR3","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.cam.2013.02.009","volume":"249","author":"NJ Ford","year":"2013","unstructured":"Ford, N.J., Rodrigues, M.M., Xiao, J., Yan, Y.: Numerical analysis of a two-parameter fractional telegraph equation. J. Comput. Appl. Math. 249, 95\u2013106 (2013)","journal-title":"J. Comput. Appl. Math."},{"key":"33_CR4","doi-asserted-by":"crossref","first-page":"454","DOI":"10.2478\/s13540-011-0028-2","volume":"14","author":"NJ Ford","year":"2011","unstructured":"Ford, N.J., Xiao, J., Yan, Y.: A finite element method for time fractional partial differential equations. Fract. Calc. Appl. Anal. 14, 454\u2013474 (2011)","journal-title":"Fract. Calc. Appl. Anal."},{"key":"33_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2478\/cmam-2012-0009","volume":"12","author":"NJ Ford","year":"2012","unstructured":"Ford, N.J., Xiao, J., Yan, Y.: Stability of a numerical method for space-time-fractional telegraph equation. Comput. Methods Appl. Math. 12, 1\u201316 (2012)","journal-title":"Comput. Methods Appl. Math."},{"key":"33_CR6","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.apnum.2005.02.008","volume":"56","author":"MM Meerschaert","year":"2006","unstructured":"Meerschaert, M.M., Tadjeran, C.: Finite difference approximations for two-sided space-fractional partial differential equations. Appl. Numer. Math. 56, 80\u201390 (2006)","journal-title":"Appl. Numer. Math."},{"issue":"2","key":"33_CR7","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1007\/s10543-013-0443-3","volume":"54","author":"Y Yan","year":"2014","unstructured":"Yan, Y., Pal, K., Ford, N.J.: Higher order numerical methods for solving frational differential equations. BIT Numer. Math. 54(2), 555\u2013584 (2014). doi:10.1007\/s10543-013-0443-3","journal-title":"BIT Numer. Math."},{"issue":"3S","key":"33_CR8","first-page":"1","volume":"5","author":"Y Dimitrov","year":"2014","unstructured":"Dimitrov, Y.: Numerical approximations for fractional differential equations. J. Frac. Calc. Appl. 5(3S), 1\u201345 (2014)","journal-title":"J. Frac. Calc. Appl."},{"key":"33_CR9","doi-asserted-by":"publisher","first-page":"558","DOI":"10.1002\/num.20112","volume":"22","author":"VJ Ervin","year":"2006","unstructured":"Ervin, V.J., Roop, J.P.: Variational formulation for the stationary fractional advection dispersion equation. Numer. Methods Partial Differ. Equ. 22, 558\u2013576 (2006)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"33_CR10","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1002\/num.20169","volume":"23","author":"VJ Ervin","year":"2007","unstructured":"Ervin, V.J., Roop, J.P.: Variational solution of fractional advection dispersion equations on bounded domains in $$\\mathbb{R}^{d}$$. Numer. Methods Partial Differ. Equ. 23, 256\u2013281 (2007)","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"33_CR11","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1137\/050642757","volume":"45","author":"VJ Ervin","year":"2007","unstructured":"Ervin, V.J., Heuer, N., Roop, J.P.: Numerical approximation of a time dependent nonlinear, space-fractional diffusion equation. SIAM J. Numer. Anal. 45, 572\u2013591 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"33_CR12","doi-asserted-by":"publisher","first-page":"1230014","DOI":"10.1142\/S0218127412300145","volume":"22","author":"CP Li","year":"2012","unstructured":"Li, C.P., Zeng, F.: Finite difference methods for fractional differential equations. Int. J. Bifurc. Chaos 22, 1230014 (2012)","journal-title":"Int. J. Bifurc. Chaos"},{"key":"33_CR13","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/j.cam.2003.09.028","volume":"166","author":"F Liu","year":"2004","unstructured":"Liu, F., Anh, V., Turner, I.: Numerical solution of space fractional Fokker-Planck equation. J. Comp. Appl. Math. 166, 209\u2013219 (2004)","journal-title":"J. Comp. Appl. Math."},{"key":"33_CR14","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.cam.2004.01.033","volume":"172","author":"MM Meerschaert","year":"2004","unstructured":"Meerschaert, M.M., Tadjeran, C.: Finite difference approximations for fractional advection-dispersion flow equations. J. Comput. Appl. Math. 172, 65\u201377 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"33_CR15","first-page":"359","volume":"3","author":"I Podlubny","year":"2000","unstructured":"Podlubny, I.: Matrix approach to discrete fractional calculus. Fract. Calc. Appl. Anal. 3, 359\u2013386 (2000)","journal-title":"Fract. Calc. Appl. Anal."},{"key":"33_CR16","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/j.cam.2005.06.005","volume":"193","author":"JP Roop","year":"2006","unstructured":"Roop, J.P.: Computational aspects of FEM approximation of fractional advection dispersion equations on bouinded domains in $$\\mathbb{R}^{2}$$. J. Comput. Appl. Math. 193, 243\u2013268 (2006)","journal-title":"J. Comput. Appl. Math."},{"key":"33_CR17","doi-asserted-by":"publisher","first-page":"850","DOI":"10.1093\/imamat\/hxn033","volume":"73","author":"S Shen","year":"2008","unstructured":"Shen, S., Liu, F., Anh, V., Turner, I.: The fundamental solution and numerical solution of the Riesz fractional advection-dispersion equation. IMA J. Appl. Math. 73, 850\u2013872 (2008)","journal-title":"IMA J. Appl. Math."},{"key":"33_CR18","doi-asserted-by":"publisher","first-page":"4038","DOI":"10.1016\/j.jcp.2009.02.011","volume":"228","author":"E Sousa","year":"2009","unstructured":"Sousa, E.: Finite difference approximations for a fractional advection diffusion problem. J. Comput. Phys. 228, 4038\u20134054 (2009)","journal-title":"J. Comput. Phys."},{"key":"33_CR19","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/j.jcp.2005.08.008","volume":"213","author":"C Tadjeran","year":"2006","unstructured":"Tadjeran, C., Meerschaert, M.M., Scheffler, H.: A second-order acurate numerical approximation for the fractional diffusion equation. J. Comput. Phys. 213, 205\u2013213 (2006)","journal-title":"J. Comput. Phys."},{"key":"33_CR20","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1016\/j.apm.2009.04.006","volume":"34","author":"Q Yang","year":"2010","unstructured":"Yang, Q., Liu, F., Turner, I.: Numerical methods for fractional partial differential equations with Riesz space fractional derivatives. Appl. Math. Model. 34, 200\u2013218 (2010)","journal-title":"Appl. Math. Model."}],"container-title":["Lecture Notes in Computer Science","Finite Difference Methods,Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-20239-6_33","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T01:45:18Z","timestamp":1676943918000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-20239-6_33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319202389","9783319202396"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-20239-6_33","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"17 June 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}