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Difference methods of order two and four for systems of mildly nonlinear biharmonic problems of the second kind in two space dimensions
Author(s) -
Mohanty R. K.,
Pandey P. K.
Publication year - 1996
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199611)12:6<707::aid-num4>3.0.co;2-w
Subject(s) - biharmonic equation , mathematics , invertible matrix , nonlinear system , order (exchange) , space (punctuation) , domain (mathematical analysis) , mathematical analysis , boundary value problem , boundary (topology) , scheme (mathematics) , pure mathematics , physics , finance , quantum mechanics , economics , linguistics , philosophy
In this article, we report two sets of finite difference methods of order two and four over a rectangular domain for the efficient numerical integration of the system of two‐dimensional nonlinear elliptic biharmonic problems of the second kind. Second‐order derivatives of the solutions are obtained as byproducts of the methods. We use only 9 grid points and do not require fictitious points in order to approximate the boundary conditions. In numerical experiments, the new second‐ and fourth‐order formulas are compared with the exact solutions both in singular and nonsingular cases. © 1996 John Wiley & Sons, Inc.