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A Novel Numerical Method of for Three-Dimensional Non-Linear Triharmonic Equations

Published online by Cambridge University Press:  20 August 2015

R. K. Mohanty ,
M. K. Jain  and
B. N. Mishra
R. K. Mohanty*
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi-110 007, India
M. K. Jain
Affiliation:
Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi-110 016, India
B. N. Mishra*
Affiliation:
Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar-751 004, India
*
Corresponding author.Email address:rmohanty@maths.du.ac.in
Email address:bn_misramath@hotmail.com
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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.

Keywords

65N0602.60.Lj02.70.BfFinite differencesthree dimensional non-linear triharmonic equationsfourth order compact discretizationLaplacianbiharmonicmaximum absolute errors
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 5 , November 2012 , pp. 1417 - 1433
Copyright
Copyright © Global Science Press Limited 2012

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