Novel and accurate Gegenbauer spectral tau algorithms for distributed order nonlinear time-fractional telegraph models in multi-dimensions. (English) Zbl 1508.65138
This article is concerned with numerical approximations to the multi-dimensional distributed-order nonlinear time-fractional telegraph equations models. The approach relies on the use of shifted Gegenbauer polynomials. The proposed method takes full advantage of the nonlocal nature of distributed order fractional differential operators. Error estimations are obtained. Also, several numerical experiments are included to support the utility of the proposed algorithm.
Reviewer: Marius Ghergu (Dublin)
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 26A33 | Fractional derivatives and integrals |
| 35R11 | Fractional partial differential equations |
Keywords:
distributed order; operational matrices; nonlinear time-fractional telegraph models; spectral tau method; Gegenbauer polynomialsReferences:
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