Block implicit Adams methods for fractional differential equations

被引:11
|
作者
Biala, T. A. [1 ]
Jator, S. N. [2 ]
机构
[1] Jigawa State Univ, Dept Math & Comp Sci, Kafin Hausa, Kafin Hausa, Nigeria
[2] Austin Peay State Univ, Dept Math & Stat, Clarksville, TN 37044 USA
关键词
Fractional differential equations; Caputo derivatives; Adams methods; Initial value problems; Fractional partial differential equations; VOLTERRA INTEGRAL-EQUATIONS; MULTISTEP METHODS;
D O I
10.1016/j.chaos.2015.10.007
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we present a family of Implicit Adams Methods (IAMs) for the numerical approximation of Fractional Initial Value Problems (FIVP) with derivatives of the Caputo type. A continuous representation of the k-step IAM is developed via the interpolation and collocation techniques and adapted to cope with the integration of FIVP. This is achieved by combining the k-step IAM with (k - 1) additional methods obtained from the same continuous scheme and applying them as numerical integrators in a block-by-block fashion. We also investigate the stability properties of the block methods and the regions of absolute stability of the methods are plotted in the complex plane. The block methods are tested on numerical examples including large systems resulting from the semi-discretization of one-dimensional fractional heat-like partial differential equations. (C) 2015 Elsevier Ltd. All rights reserved,
引用
收藏
页码:365 / 377
页数:13
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