Time-fractional nonlinear Swift-Hohenberg equation: Analysis and numerical simulation

Abstract

In this paper, a new scheme based on the exponential fitting technique is presented for solving the nonlinear time-fractional Swift-Hohenberg equation, where the first and second-order derivatives are replaced by Caputo fractional derivative. The exponential fitting technique depends on a parameter that led to getting high-order accuracy. The convergence and unconditional stability will be discussed using the Fourier method and the analysis is built on uniform and nonuniform time steps, to solve initial singularity by using the graded meshes. Applicability and theoretical results will be demonstrated and enhanced with numerical examples.