Advanced shifted first-kind Chebyshev collocation approach for solving the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel
AG Atta, YH Youssri - Computational and Applied Mathematics, 2022 - Springer
Computational and Applied Mathematics, 2022•Springer
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 …
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 …
Abstract
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.
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