A novel hybrid approach for computing numerical solution of the time-fractional nonlinear one and two-dimensional partial integro-differential equation

Abstract

In this article, we develop a computational technique for solving the nonlinear time-fractional one and two-dimensional partial integro-differential equation with a weakly singular kernel. For the approximation of spatial derivatives, we apply the Haar wavelets collocation method whereas, for the time-fractional derivative, we use the nonstandard finite difference (NSFD) scheme. We implement the quasilinearization technique to deal with the nonlinear term and product trapezoidal rule for the approximation of integral term. To demonstrate the accuracy of the method, we investigate several test problems and report the accuracy of the method. The convergence and stability of the proposed method are also discussed.