Advanced shifted first-kind Chebyshev collocation approach for solving the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel. (English) Zbl 1513.65398
Summary: This research apparatuses an approximate spectral method for the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel (TFPIDE). The main idea of this approach is to set up a new Hilbert space that satisfies the initial and boundary conditions. The new spectral collocation approach is applied to obtain precise numerical approximation using new basis functions based on shifted first-kind Chebyshev polynomials (SCP1K). Furthermore, we support our study by a careful error analysis of the suggested shifted first-kind Chebyshev expansion. The results show that the new approach is very accurate and effective.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 45K05 | Integro-partial differential equations |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 35R09 | Integro-partial differential equations |
| 41A50 | Best approximation, Chebyshev systems |
| 26A33 | Fractional derivatives and integrals |
| 35R11 | Fractional partial differential equations |
Keywords:
nonlinear time-fractional partial integro-differential equation with a weakly singular kernel; first-kind Chebyshev polynomials; collocation method; error analysisReferences:
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