A Novel Numerical Method of <em>O</em>(<em>h</em><sup>4</sup> ) for Three-Dimensional Non-Linear Triharmonic Equations
Year: 2012
Communications in Computational Physics, Vol. 12 (2012), Iss. 5 : pp. 1417–1433
Abstract
In this article, we present two new novel finite difference approximations of order two and four, respectively, for the three dimensional non-linear triharmonic partial differential equations on a compact stencil where the values of u, ∂2u/∂n2 and ∂4u/∂n4 are prescribed on the boundary. We introduce new ideas to handle the boundary conditions and there is no need to discretize the derivative boundary conditions. We require only 7- and 19-grid points on the compact cell for the second and fourth order approximation, respectively. The Laplacian and the biharmonic of the solution are obtained as by-product of the methods. We require only system of three equations to obtain the solution. Numerical results are provided to illustrate the usefulness of the proposed methods.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.080910.060112a
Communications in Computational Physics, Vol. 12 (2012), Iss. 5 : pp. 1417–1433
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17