Volume 12, Issue 5
A Novel Numerical Method of O(h4 ) for Three-Dimensional Non-Linear Triharmonic Equations

R. K. Mohanty, M. K. Jain & B. N. Mishra

Commun. Comput. Phys., 12 (2012), pp. 1417-1433.

Published online: 2012-12

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  • 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 areprescribedon 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.


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