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A Novel Numerical Method of <em>O</em>(<em>h</em><sup>4</sup> ) for Three-Dimensional Non-Linear Triharmonic Equations

A Novel Numerical Method of <em>O</em>(<em>h</em><sup>4</sup> ) for Three-Dimensional Non-Linear Triharmonic Equations
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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.

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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

Keywords:   

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