Global Error Estimation in the Method of Lines for Parabolic Equations

A method is described for obtaining an indication of the error in the numerical solution of parabolic partial differential equations using the method of lines. The error indicator is derived by using a combination of existing global error estimating algorithms for initial value problems in ordinary differential equations with estimates for the PDE truncation error. An implementation of the algorithm is described and numerical examples are used to illustrate the reliability of the error estimates that are obtained.