Error analysis of modified schemes for time-fractional Cable equation

Abstract

Abstract: Error analysis of the modified second-order backward difference scheme for the time-fractional Cable equation is carried out. By using continuous Laplace transform and inverse Laplace transform, the exact solution of the equation is obtained, and the finite element semidiscrete solution is obtained similarly. Then Lubich's correction method is used to get the modified form of the fractional differential equation. The discrete solutions of the Cable equation are obtained by means of the discrete Laplace transform and the inverse Laplace transform. Finally, the error estimates under the norm are discussed and the second order of convergence is obtained. Numerical results verification is finally performed to validate the theoretical findings discussed here, which proved that it is better than the first order convergence without modification.

Key words: fractional Cable equation, Riemann-Liouville fractional derivative, Laplace transform, Nonsmooth data error estimation

CLC Number:

O241.8

WU Xiao-lei, YANG Yan, YAN Yu-bin. Error analysis of modified schemes for time-fractional Cable equation[J]. Journal of Lanzhou University of Technology, 2023, 49(1): 158-163.

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