Abstract
AbstractWe present a nine‐point fourth‐order finite difference method for the nonlinear second‐order elliptic differential equation Auxx + Buyy = f(x, y, u, ux, uy) on a rectangular region R subject to Dirichlet boundary conditions u(x, y) = g(x, y) on ∂R. We establish, under appropriate conditions O(h4)‐convergence of the finite difference scheme. Numerical examples are given to illustrate the method and its fourth‐order convergence.
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