A comparison of time marching schemes for the transient heat conduction equation

Abstract

Abstract This paper investigates the phenomenon of ‘noise’ which is common in most time‐dependent problems. The emphasis is on the achievable accuracy that is obtained with various time‐stepping algorithms and how this can be improved if noise is artificially damped to an acceptable level. A series of experiments are made where the space domain is discretized using the finite element method and the variation with time is approximated by several finite difference methods. The conclusion is reached that the Crank–Nicolson scheme with a simple averaging process is superior to the other methods investigated.