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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

DOI: 10.4208/cicp.080910.060112a

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 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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@Article{CiCP-12-1417, author = {R. K. Mohanty, M. K. Jain and B. N. Mishra}, 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} }
TY - JOUR T1 - A Novel Numerical Method of O(h4 ) for Three-Dimensional Non-Linear Triharmonic Equations AU - R. K. Mohanty, M. K. Jain & B. N. Mishra JO - Communications in Computational Physics VL - 5 SP - 1417 EP - 1433 PY - 2012 DA - 2012/12 SN - 12 DO - http://doi.org/10.4208/cicp.080910.060112a UR - https://global-sci.org/intro/article_detail/cicp/7340.html KW - AB -

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.

R. K. Mohanty, M. K. Jain and B. N. Mishra. (2012). A Novel Numerical Method of O(h4 ) for Three-Dimensional Non-Linear Triharmonic Equations. Communications in Computational Physics. 12 (5). 1417-1433. doi:10.4208/cicp.080910.060112a
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