Bernstein polynomials for solving fractional heat- and wave-like equations. (English) Zbl 1312.65168
Summary: In this paper, a novel numerical analysis is introduced and performed to obtain the numerical solution of the fractional heat- and wave-like equations. A general formulation for the Bernstein fractional derivatives operational matrix is given. In this approach, a truncated Bernstein series together with the Bernstein operational matrix of fractional derivatives are used to reduce the solution of fractional differential problems to the solution of a system of algebraic equations. Numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques and to compare with the existing results.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
| 26A33 | Fractional derivatives and integrals |
| 41A10 | Approximation by polynomials |
| 45K05 | Integro-partial differential equations |
| 41A30 | Approximation by other special function classes |
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