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A comparison of two kinds of finite difference schemes for space-time fractional convection-diffusion equations. (English) Zbl 1374.65147

Summary: Two implicit finite difference schemes were developed for solving one dimensional space-time fractional convection-diffusion equations with variable coefficients on a finite domain, and our purpose was to compare these two finite difference schemes in terms of the accuracy and convergence order of the scheme. We took advantage of the central difference at two different points respectively when we discretized the temporal \(\alpha\)-order derivative term using Caputo fractional order derivative. The spatial \(\beta\)-order derivative term was discretized by using a shifted Grunwald formula. Analysis of stability and convergence of the methods was done. Numerical examples with known exact solution were used to verify and compare the finite difference schemes.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
35K20 Initial-boundary value problems for second-order parabolic equations
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