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Highly accurate technique for solving distributed-order time-fractional-sub-diffusion equations of fourth order. (English) Zbl 1449.65270

Summary: This paper presents a new method for calculating the numerical solution of distributed-order time-fractional-sub-diffusion equations (DO-TFSDE) of fourth order. The method extends the shifted fractional Jacobi (SFJ) collocation scheme for discretizing both the time and space variables. The approximate solution is expressed as a finite expansion of SFJ polynomials whose derivatives are evaluated at the SFJ quadrature points. The process yields a system of algebraic equations that are solved analytically. The new method is compared with alternative numerical algorithms when solving different types of DO-TFSDE. The results show that the proposed method exhibits superior accuracy with an exponential convergence rate.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
41A55 Approximate quadratures
35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
65D32 Numerical quadrature and cubature formulas
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