×

On the numerical solution of fractional parabolic partial differential equations with the Dirichlet condition. (English) Zbl 1248.65085

Summary: The first and second order of accuracy stable difference schemes for the numerical solution of the mixed problem for the fractional parabolic equation are presented. Stability and almost coercive stability estimates for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of one-dimensional fractional parabolic partial differential equations.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
35K99 Parabolic equations and parabolic systems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Mathematics in Science and Engineering 198 (1999)
[2] (1993)
[3] DOI: 10.1016/S0304-0208(06)80001-0
[4] DOI: 10.1016/j.amc.2003.11.026 · Zbl 1062.65073
[5] DOI: 10.1007/978-3-642-14574-2 · Zbl 1215.34001
[6] DOI: 10.1016/j.cam.2010.10.054 · Zbl 1217.65154
[7] DOI: 10.1016/S0096-3003(03)00739-2 · Zbl 1060.65070
[8] Pure Mathematics and Applications 12 (3) pp 296– (2001)
[9] DOI: 10.1590/S0101-82052004000100002 · Zbl 1213.34025
[10] Stability results for fractional differential equations with applications to control processing 2 (1996)
[11] Quarterly Journal of Mathematics 42 pp 369– (1910)
[12] Fractional calculus: some basic problems in continuum and statistical mechanics pp 291– (1997)
[13] DOI: 10.1016/j.amc.2010.11.017 · Zbl 1221.65212
[14] DOI: 10.1016/j.aml.2011.02.002 · Zbl 1217.34006
[15] DOI: 10.1155/2011/161246 · Zbl 1217.34124
[16] DOI: 10.1016/j.cnsns.2011.06.008 · Zbl 1248.35225
[17] Advances in Difference Equations 2011 (2011)
[18] Fixed Point Theory and Applications 2011 (2011)
[19] DOI: 10.1142/S0219530511001753 · Zbl 1216.34005
[20] Electronic Journal of Qualitative Theory of Differential Equations 13 pp 1– (2011)
[21] Advances in Difference Equations 2009 (2009)
[22] Advances in Difference Equations 2010 (2010)
[23] DOI: 10.1016/j.nonrwa.2010.01.002 · Zbl 1248.34004
[24] Nonlinear Analysis 75 (6) pp 3268– (2011)
[25] Abstract and Applied Analysis 2012 (2012)
[26] Abstract and Applied Analysis 2012 (2012)
[27] Abstract and Applied Analysis 2012 (2012)
[28] Abstract and Applied Analysis 2012 (2012)
[29] Matematica e Applicazioni 9 (4) pp 245– (1999)
[30] Boundary Value Problems (1) pp 9– (2005)
[31] DOI: 10.1007/978-3-0348-9234-6
[32] (1975)
[33] (1994)
[34] Trudy Naucno-Issledovatel’skogi Instituta Matematiki VGU 14 pp 68– (1975)
[35] DOI: 10.1016/j.jmaa.2009.04.012 · Zbl 1175.26004
[36] (4) pp 117– (1970)
[37] (1989)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.