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

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. & COPY; 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This article discusses an efficient numerical method for solving nonlinear time-fractional integro-partial differential initial-boundary-value problems. The non-linearity is tackled using the Newton linearization process. The non-symmetric interior penalty Galerkin method is applied for the spatial variable, and a semi-discrete problem is obtained in the time variable. By using L1-scheme and L2-scheme for the time-fractional derivative, and trapezoidal rule for the integral term, a fully-discrete scheme is derived.