Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay

Abstract

The purpose of this paper is to develop a numerical scheme for the two-dimensional fourth-order fractional subdiffusion equation with variable coefficients and delay. Using the L2−1σ approximation of the time Caputo derivative, a finite difference method with second-order accuracy in the temporal direction is achieved. The novelty of this paper is to introduce a numerical scheme for the problem under consideration with variable coefficients, nonlinear source term, and delay time constant. The numerical results show that the global convergence orders for spatial and time dimensions are approximately fourth order in space and second-order in time.

Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain

“…Spectral techniques (see, e.g., previous works [42][43][44][45][46][47][48][49] ) are approaches used in applied mathematics and scientific computing to numerically approximate the solutions of both linear and nonlinear differential and integral equations. The spectral tau, Galerkin, and collocation schemes are three well-known types of spectral techniques.…”

Design and analysis of a high order computational technique for time‐fractional Black–Scholes model describing option pricing

“…One of the widely used techniques to approximate the temporal fractional Caputo derivative is the classical L1-scheme which has the truncation error of order O(𝜏 2 − 𝛼 ), for instance, see. [31][32][33][34][35] Further, the L2 − 1 𝜎 scheme, proposed by Alikhanov, 36 were used in 37,38 to discretize temporal fractional Caputo derivative, which provides second-order global convergence in the temporal direction. The goal of this paper is to present an efficient and reliable numerical computational scheme to solve the TBS model ( 1)-(3).…”