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On the validity and stability of the method of lines for the solution of partial differential equations. (English) Zbl 0619.65105

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.
Reviewer: J.M.Sanz-Serna

MSC:

65N40 Method of lines for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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