Maximum modulus principle estimates for one dimensional fractional diffusion equation. (English) Zbl 1349.35417
Summary: We present scheme I for solving one-dimensional fractional diffusion equation with variable coefficients based on the maximum modulus principle and two Grunwald approximations. Scheme II is obtained by using classic Crank-Nicolson approximations in order to improve the time convergence. The two schemes are proved to be unconditionally stable and second-order accuracy in spatial grid size for the problem with order of fractional derivative belonging to \([(\sqrt{17} - 1)/2, 2]\) using the maximum modulus principle. A numerical example is given to confirm the theoretical analysis result.
MSC:
| 35R11 | Fractional partial differential equations |
| 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 |
Keywords:
the maximum modulus principle; Grunwald approximation; finite difference scheme; fractional diffusion equation; numerical analysisReferences:
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