On the Behavior of Combination High-Order Compact Approximations with Preconditioned Methods in the Diffusion-Convection Equation

Abstract

In this paper, a family of high-order compact finite difference methods in combination preconditioned methods are used for solution of the Diffusion-Convection equation. We developed numerical methods by replacing the time and space derivatives by compact finite-difference approximations. The system of resulting nonlinear finite difference equations are solved by preconditioned Krylov subspace methods. Numerical results are given to verify the behavior of high-order compact approximations in combination preconditioned methods for stability, convergence. Also, the accuracy and efficiency of the proposed scheme are considered

Method of approximations for the convection-dominated anomalous diffusion equation in a rectangular plate using high-resolution compact discretization

“…Applications of compact formulation in fractional differential equations have been discussed earlier in [18] . Solution techniques with compact discretization combined with B-spline and preconditioned methods for Fisher's equation, advection-diffusion equations, and diffusion-convection equation have been described in [19] , [20] , [21] .…”