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 = {https://global-sci.com/article/80826/a-novel-numerical-method-of-emoememhemsup4sup-for-three-dimensional-non-linear-triharmonic-equations} }