A Novel Higher-Order Time Integration Method Using the Modified Explicit Green's Approach for Linear Parabolic Problems

Abstract

This article is concerned with the development of a novel higher-order time-marching scheme applied to the semidiscrete transient diffusion equation of parabolic type. Adopting the modified explicit Green's approach (ExGAM) to integrate on time, an optimized substep procedure is proposed to compute the modified Green's matrix at time t = Δt. This modified Green's matrix is evaluated numerically by the generalized θ method. Thereby the present new method retains some advantages of the standard θ method, but with an arbitrary order of accuracy. The high accuracy of the proposed scheme is tested by two examples and compared with exact benchmark solutions.