New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation. (English) Zbl 1173.26006

Zhuang, P.; Liu, Fawang; Anh, V.; Turner, I.

SIAM J. Numer. Anal. 46, No. 2, 1079-1095 (2008).

Since the effective numerical methods and suporting error analyses for the anomalous subdiffusion equation (ASub-DE) are limited, the authors have solved and analyzed it by the introduction of an implicit numerical method and new solution techniques. The implicit numerical method (abbreviated as INM) is given in Section 2, the stability and convergence analyses for INM are given in Sections 3 and 4 and the new solution techniques occupies Section 5. Numerical results given in Section 6 appear to be interesting, particularly the Example 2, Equation (6.4). It may not be out of place to suggest reading K. S. Miller and B. Ross [An introduction to the fractional calculus and fractional differential equations. New York: John Wiley & Sons (1993; Zbl 0789.26002)] in regard to various types of differential equations solved by fractional calculus.

Reviewer: P. K. Banerji (Jodhpur)

MSC:

26A33	Fractional derivatives and integrals
45K05	Integro-partial differential equations
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

implict numerical method; fractional derivative; fractional integro-differential equations; convergence