A collocation method based on reproducing kernel for a modified anomalous subdiffusion equation

Numerical Methods for Partial Differential Equations

Volumn 30, Issue 1, 2014, Pages 289-300

  Jiang, Wei ^a   Chen, Zhong ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

approximate solution; collocation method; reproducing kernel; subdiffusion equation

Indexed keywords

ANOMALOUS SUBDIFFUSION EQUATION; APPROXIMATE SOLUTION; COLLOCATION METHOD; NUMERICAL EXPERIMENTS; REPRODUCING KERNEL; SUBDIFFUSION EQUATIONS; SYSTEM OF LINEAR EQUATIONS;

PARTIAL DIFFERENTIAL EQUATIONS;

NUMERICAL METHODS;

EID: 84889238605     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.21809     Document Type: Article

References (24)

1. I. Sokolov, and, J. Klafter, From diffusion to anomalous diffusion: a century after Einsteins Brownian motion, Chaos 15 (2005), 26-103.
2. A. V. Chechkin, R. Gorenflo, I. M. Sokolov, and, V. Yu. Gonchar, Distributed order time fractional diffusion equation, Frac Calc Appl Anal 6 (2003), 259-279.
3. I. M. Sokolov, A. V. Checkin, and, J. Klafter, Distributed-order fractional kinetics, Acta Phys Pol B 35 (2004), 13-23.
4. E. Scalas, R. Gorenflo, and, F. Mainardi, Fractional calculus and continuoustime finance, Physica A 284 (2000), 376-384.
5. F. Mainardi, M. Raberto, R. Gorenflo, and, E. Scalas, Fractional calculus and continuous-time finance II: The waiting-time distribution, Physica A 287 (2000), 468-481. (Pubitemid 32034791)
6. M. Raberto, E. Scalas, and, F. Mainardi, Waiting-times and returns in high frequency financial data: An empirical study, Physica A 314 (2002), 749-755.
7. E. Scalas, R. Gorenflo, F. Mainardi, M. Mantelli, and, M. Raberto, Anomalous waiting times in high-frequency financial data, Quant Financ 4 (2000), 695-702. (Pubitemid 40659504)
8. E. Scalas, Five years of continuous-time random walks in econophysics, A. Namatame, editor, Proceedings of WEHIA 2004, Kyoto, 2004.
9. E. Scalas, R. Gorenflo, F. Mainardi, and, M. M. Meerschaert, Speculative option valuation and the fractional diffusion equation, J. Sabatier and, J. TenreiroMachado, editors, Proceedings of the IFAC Workshop on Fractional Differentiation and its Applications, Bordeaux, 2004.
10. E. Scalas, The application of continuous-time random walks in finance and economics, Physica A 362 (2006), 225-239. (Pubitemid 43234049)
11. J. Masoliver, and, M. Montero, Continuous-time random-walk model for financial distributions, Phys Rev E 67 (2003), 21-112.
12. J. Masoliver, M. Montero, J. Perello, and, G. Weiss, The CTRW in finance:direct and inverse problems with some generalizations and extensions, Physica A 379 (2007), 151-167. (Pubitemid 46464002)
13. J. Masoliver, M. Montero, J. Perello, and, G. H. Weiss, The continuous time random walk formalism in financial markets, J Econ Behav Organ 61 (2006), 577-598. (Pubitemid 44848158)
14. T. A. M. Langlands, Solution of a modified fractional diffusion equation, Physica A 367 (2006), 136-144. (Pubitemid 43674289)
15. W. Jiang, and, Y. Z. Lin, Approximate solution of the fractional advection dispersion equation, Comput Phys Commun 183 (2010), 557-561.
16. W. Jiang, and, Y. Z. Lin, Representation of exact solution for the time fractional telegraph equation in the reproducing kernel space, Commun Nonlinear Sci Numer Simul 16 (2011), 3639-3645.
17. Y. Z. Lin, and, W. Jiang, Numerical method for Stokes' first problem for a heated generalized second grade fluid with fractional derivative, Numer Methods Partial Differ Equ 27 (2011), 1599-1609.
18. Q. Liu, F. Liu, I. Turner, and, V. Anh, Finite element approximation for a modified anomalous subdiffusion equation, Appl Math Model 35 (2011), 4103-4116.
19. L. N. Song, and, W. G. Wang, A new improved adomian decomposition method and its application to fractional differential equations, Appl Math Model 37 (2013), 1590-1598.
20. M. G. Sakar, F. Erdogan, and, A. Yildirim, Variational iteration method for the time-fractional Fornberg-Whitham equation, Comput Math Appl 63 (2012), 1382-1388.
21. I. M. Sokolov, A.V. Chechkin, and, J. Klafter, Distributed-order fractional kinetics, Acta Phys Pol B 35 (2004), 1323-1341.
22. Y. F. Zhou, M. G. Cui, and, Y. Z. Lin, Numerical algorithm for parabolic problems with non-classical conditions, J Comput Appl Math 230 (2009), 770-780.
23. M. G. Cui, and, Y. Z. Lin, Nonlinear numerical analysis in the reproducing kernel space, Nova Science Publishers, New York, 2008.
24. Z. Chen, C. H. Wang, and, Y. F. Zhou, A new method for solving Cauchy type singular integral equations of the second kind, Int J Comput Math 87 (2010), 2076-2087.