We solve nonlinear elliptic PDEs by stable finite difference schemes of high order on a uniform meshgrid. These schemes have been introduced in [1] in the class of Boundary Value Methods (BVMs) to solve two-point Boundary Value Problems (BVPs) for second order ODEs and are high order generalizations of classical finite difference schemes for the first and second derivatives. Numerical results for a minimal surface problem and for the Gent model in nonlinear elasticity are presented.
High order finite difference schemes for the solution of elliptic PDEs
AMODIO, Pierluigi;
2004-01-01
Abstract
We solve nonlinear elliptic PDEs by stable finite difference schemes of high order on a uniform meshgrid. These schemes have been introduced in [1] in the class of Boundary Value Methods (BVMs) to solve two-point Boundary Value Problems (BVPs) for second order ODEs and are high order generalizations of classical finite difference schemes for the first and second derivatives. Numerical results for a minimal surface problem and for the Gent model in nonlinear elasticity are presented.File in questo prodotto:
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