Balancing Space and Time Errors in the Method of Lines for Parabolic Equations

Abstract

A new error control strategy for the time integration in the solution of parabolic equations using the method of lines is presented. The strategy aims to approximately balance the spatial discretisation and time integration errors so that they are of the same order of magnitude, but so that the time integration error is less than the spatial discretisation error. This is achieved by making use of the individual contributions of the spatial discretisation error and the time integration error to an existing estimate of the global error in the numerical solution. The new strategy is presented in the light of this global error indicator and a comparison between the new error control strategy and a similar existing strategy is made. Numerical results are used to illustrate the performance of this strategy.