A novel time substep procedure into the classical central difference scheme to derive fourth-order methods in the complex plane

Abstract

This work is concerned with the development of new fourth-order accurate explicit time integration methods for the solution of wave propagation problems discretized by the finite element method. These novel schemes are derived from the well-known Central Difference time integration method through a proposed time substep procedure formed by either two or three complex substeps. The proposed formulation follows a different approach of standard time integration methods in the sense that results in the time domain are complex numbers, and advantages of such a distinct feature and its relation to the error are presented and discussed. A numerical analysis reveals that the proposed formulation not only enhances the stability but also increases the accuracy when compared to the classical Central Difference method; besides, the computer implementation is very straightforward. Finally, numerical examples are presented and the results are compared with the corresponding ones from other fourth-order methods in order to demonstrate the effectiveness, robustness and potentialities of the proposed formulation.