Effective numerical simulation of time fractional KdV equation with weakly singular solutions

Abstract

A second-order time-stepping method for numerically solving the linearized time fractional KdV equation (TFKDVE) whose solution has initial singularity is investigated. Alikhanov’s scheme is used to discretize the Caputo fractional derivative on temporal graded mesh, and the space is approximated by a Petrov–Galerkin spectral method. Detailed stability and error estimate of the full-discrete scheme are given, and the final error bound is [Formula: see text]-robust. Numerical examples are given to illustrate the sharpness of the error analysis.