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

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  • Maji, Sandip
  • Natesan, Srinivasan

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.

Suggested Citation

  • Maji, Sandip & Natesan, Srinivasan, 2023. "Nonsymmetric interior penalty Galerkin method for nonlinear time-fractional integro-partial differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 213(C), pages 1-17.
    • Handle: RePEc:eee:matcom:v:213:y:2023:i:c:p:1-17
    DOI: 10.1016/j.matcom.2023.05.020
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