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A New High Accuracy Off-Step Discretisation for the Solution of 2D Nonlinear Triharmonic Equations

Published online by Cambridge University Press:  28 May 2015

Swarn Singh ,
Suruchi Singh  and
R. K. Mohanty
Swarn Singh
Affiliation:
Department of Mathematics, Sri Venkateswara College, University of Delhi, New Delhi-110021, India
Suruchi Singh
Affiliation:
Department of Mathematics, Aditi Mahavidayalaya, University of Delhi, Delhi-110039, India
R. K. Mohanty*
Affiliation:
Department of Applied Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi - 110021, India
*
Corresponding author. Email Address: rmohanty@sau.ac.in
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Abstract

In this article, we derive a new fourth-order finite difference formula based on off-step discretisation for the solution of two-dimensional nonlinear triharmonic partial differential equations on a 9-point compact stencil, where the values of u,(∂2u/∂n2) and (∂4u/∂n4) are prescribed on the boundary. We introduce new ways to handle the boundary conditions, so there is no need to discretise the boundary conditions involving the partial derivatives. The Laplacian and biharmonic of the solution are obtained as a by-product of our approach, and we only need to solve a system of three equations. The new method is directly applicable to singular problems, and we do not require any fictitious points for computation. We compare its advantages and implementation with existing basic iterative methods, and numerical examples are considered to verify its fourth-order convergence rate.

Keywords

65N06High accuracy finite differencesoff-step discretisationtwo-dimensional nonlinear triharmonic equationsLaplacianbiharmonictriharmonicmaximum absolute errors
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 3 , Issue 3 , August 2013 , pp. 228 - 245
Copyright
Copyright © Global-Science Press 2013

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