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.
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Work supported by GNCS and MIUR (60% project). The work of I. S. was partially supported by the Progetto Giovani Ricercatori Università di Lecce-MIUR 2001/2002.
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References
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© 2004 Springer-Verlag Berlin Heidelberg
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Amodio, P., Sgura, I. (2004). High Order Finite Difference Schemes for the Solution of Elliptic PDEs. In: Zhang, J., He, JH., Fu, Y. (eds) Computational and Information Science. CIS 2004. Lecture Notes in Computer Science, vol 3314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30497-5_1
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DOI: https://doi.org/10.1007/978-3-540-30497-5_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24127-0
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