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. © Springer-Verlag 2004.
CITATION STYLE
Amodio, P., & Sgura, I. (2004). High order finite difference schemes for the solution of elliptic PDEs. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3314, 1–6. https://doi.org/10.1007/978-3-540-30497-5_1
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