Numerical solution of time fractional non-linear neutral delay differential equations of fourth-order

Abstract

In this paper, we present a numerical technique for the solution of a class of time fractional nonlinear neutral delay sub-diffusion differential equation of fourth order with variable coefficients. We constructed a numerical scheme which is of second-order convergence in time and is based on L2-1σ formula for the temporal variable. The stability of the scheme is proved using discrete energy method considering several auxiliary assumptions and then we showed that our scheme is convergent in L 2 norm with convergence order O(τ 2 + h 4), where τ and h are temporal and space mesh sizes respectively. In the end, we provide some numerical experiments to validate the theoretical results.

Compact Difference Method for Time-Fractional Neutral Delay Nonlinear Fourth-Order Equation

“…Then in [37], Zhang et al constructed a compact finite difference scheme for fourth order fractional diffusion equations with the second Dirichlet boundary condition by using the L2-1σ formula to approximate the time fractional derivative and the compact operator to approximate spatial fourth order derivative. Delay differential equations are widely used in many fields, such as population ecology, cell biology, control theory, economics and so on [38] [39] [40]. In [38] [39] Sarita Ndal et al discuss finite difference scheme for one-dimensional time fractional fourth-order diffusion equation, which contains a nonlinear source function with time delay and a fourth-order space delay term.…”

“…Delay differential equations are widely used in many fields, such as population ecology, cell biology, control theory, economics and so on [38] [39] [40]. In [38] [39] Sarita Ndal et al discuss finite difference scheme for one-dimensional time fractional fourth-order diffusion equation, which contains a nonlinear source function with time delay and a fourth-order space delay term. The unique solva-bility, stability and convergence of the scheme are proved.…”