Nonsymmetric interior penalty Galerkin method for nonlinear time-fractional integro-partial differential equations

Sandip Maji and Srinivasan Natesan

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 213, issue C, 1-17

Abstract: This article discusses an efficient numerical method for solving nonlinear time-fractional integro-partial differential initial–boundary-value problems. To tackle the non-linearity of the problem, we first use the Newton linearization process. Then we apply the non-symmetric interior penalty Galerkin method for the spatial variable, and obtain a semi-discrete problem in the time variable. Finally, to obtain the fully-discrete scheme, we use both L1-scheme and L2-scheme for time-fractional derivative, and trapezoidal rule for integral term in the semi-discrete problem. We derive L2-norm stability and error estimates. The validity of the error analysis is supported by numerical experiments.

Keywords: Integro-partial differential equations; Fractional partial differential equations; Discontinuous Galerkin method; Stability; Error estimate (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:213:y:2023:i:c:p:1-17

DOI: 10.1016/j.matcom.2023.05.020

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