Numerical scheme with high order accuracy for solving a modified fractional diffusion equation. (English) Zbl 1336.65131
Summary: In recent years, some researchers have developed various numerical schemes to solve the modified fractional diffusion equation. For the numerical solutions of the modified fractional diffusion equation, there are already some important progresses. In this paper, a numerical scheme with second order temporal accuracy and fourth order spatial accuracy is developed to solve a modified fractional diffusion equation; the convergence, stability and solvability of the numerical scheme are analyzed by Fourier analysis; the theoretical results extremely consistent with the numerical experiment.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
Keywords:
modified fractional diffusion equation; numerical scheme with second order temporal accuracy and fourth order spatial accuracy; convergence; stability; solvability; Fourier analysisReferences:
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