Error bounds for approximate solutions to nonlinear ordinary differential equations

Abstract

Error bounds are provided for approximate solution of systems of nonlinear ordinary differential equations for cases where there is no known exact solution for comparison. Theorems are proved for problems of heat and mass transfer of a multicomponent system in catalyst particles under going chemical reaction. Error bounds are provided for the pointwise error as well as the effectiveness factor. Calculations based on the theorems show the orthogonal collocation method can give results which are proved accurate to 12 digits, thus providing essentially the exact solution. For problems for which the theorems have not yet been proved, the results suggest that the mean‐squared residual gives a good indication of the accuracy since the error decreases as the mean‐squared residual decreases.