On the validity and stability of the method of lines for the solution of partial differential equations

摘要

The method of lines (MOL) for the numerical solution of partial differential equations is presented. Its application to equations of the elliptic type is examined with a view to showing that the instability usually blamed on MOL has its origin in the original equation. The MOL system of ordinary differential equations is shown to be a valid representation of the partial differential equation. The effect of increasing the number of lines used is discussed. It is shown that as the number of lines is increased, the accuracy of the MOL representation of the original system increases.