Time splitting ratio in the ρ∞-Bathe time integration method for higher-order accuracy in structural dynamics and heat transfer

Abstract

Our objective in this paper is to investigate the use of the splitting ratio, γ, in the ρ∞-Bathe method to reach a higher-order accuracy in the finite element solutions of structural dynamics and heat transfer problems. We study the order of accuracy of the method for both types of analyses, and identify a real-valued γp resulting into third-order accuracy with ρ∞=(-1,1-3] and a complex-valued γi with ρ∞∈[0,1] providing at least third-order accuracy but γi with ρ∞=1 gives fourth-order accuracy. In both types of analyses, structural and heat transfer solutions, the γ values result into the same orders of convergence. To illustrate our theoretical findings, we give the results of some example solutions of structural dynamics and heat flow problems. These solutions show that more accurate response predictions can be obtained when using the more effective γ values.