Abstract
In this paper, we construct pure alternative segment explicit-implicit (PASE-I) and implicit-explicit (PASI-E) difference algorithms for time fractional reaction-diffusion equations (FRDEs). They are a kind of difference schemes with intrinsic parallelism and based on classical explicit scheme and classical implicit scheme combined with alternating segment technology. The existence and uniqueness analysis of solutions of the parallel difference schemes are given. Both the theoretical proof and the numerical experiment show that PASE-I and PASI-E schemes are unconditionally stable and convergent with second-order spatial accuracy and 2−α order time accuracy. Compared with implicit scheme and E-I (I-E) scheme, the computational efficiency of PASE-I and PASI-E schemes is greatly improved. PASE-I and PASI-E schemes have obvious parallel computing properties, which shows that the difference schemes with intrinsic parallelism in this paper are feasible to solve the time FRDEs.
Highlights
Fractional differential equations can be used to describe some physical phenomena more accurately than the classical integer order differential equations. e time fractional reaction-diffusion equations (FRDEs) play an important role in dynamical systems of physics [1, 2], bioinformatics [3, 4], image processing [5], and other research areas [6, 7]
Tadjeran et al [14] examined a second-order accurate numerical method in time and in space to solve a class of initial-boundary value fractional diffusion equations with variable coefficients
It is shown that the pure alternative segment explicit-implicit (PASE-I) scheme in this paper is equivalent to the existing implicit and E-I scheme in spatial and temporal accuracy, and the results of numerical experiments are consistent with theoretical analysis
Summary
E existence and uniqueness analysis of solutions of the parallel difference schemes are given. We construct pure alternative segment explicit-implicit (PASE-I) and implicit-explicit (PASI-E) difference algorithms for time fractional reaction-diffusion equations (FRDEs). Both the theoretical proof and the numerical experiment show that PASE-I and PASI-E schemes are unconditionally stable and convergent with second-order spatial accuracy and 2 − α order time accuracy. PASE-I and PASI-E schemes have obvious parallel computing properties, which shows that the difference schemes with intrinsic parallelism in this paper are feasible to solve the time FRDEs
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