@Article{CiCP-12-1417, author = {}, title = {A Novel Numerical Method of O(h4 ) for Three-Dimensional Non-Linear Triharmonic Equations}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {5}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.080910.060112a}, url = {http://global-sci.org/intro/article_detail/cicp/7340.html} }