On the validity and stability of the method of lines for the solution of partial differential equations
The method of lines based on the simplest finite difference replacement of \(\partial^ 2/\partial y^ 2\) is applied to the soluton of the Dirichlet problem for Laplace's equation \(\partial^ 2u/\partial x^ 2+\partial^ 2u/\partial y=0\) in a square in the (x,y)-plane. The standard Fourier series representation of the true and the numerical solutions are given and several perfunctory conclusions are drawn.
scientific article; zbMATH DE number 4005528