Asymptotic Expansions for a Class of Elliptic Difference Schemes
Copyright policy )Asymptotic Expansions for a Class of Elliptic Difference Schemes
In this paper, we derive an asymptotic expansion of the global error for Kreiss’ difference scheme for the Dirichlet problem for Poisson’s equation. This scheme, combined with a deferred correction procedure or the Richardson extrapolation technique, yields a method of accuracy at least O ( h 6.5 ) O({h^{6.5}}) in L 2 {L_2} , where h is the mesh length.
Richardson extrapolation, Error bounds for boundary value problems involving PDEs, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Deferred correction, rates of convergence, Stability and convergence of numerical methods for boundary value problems involving PDEs, asymptotic expansions
Richardson extrapolation, Error bounds for boundary value problems involving PDEs, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Deferred correction, rates of convergence, Stability and convergence of numerical methods for boundary value problems involving PDEs, asymptotic expansions
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