Go to previous page

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

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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:   

  1. Operator compact exponential approximation for the solution of the system of 2D second order quasilinear elliptic partial differential equations

    Mohanty, R. K. | Manchanda, Geetan | Khan, Arshad

    Advances in Difference Equations, Vol. 2019 (2019), Iss. 1

    https://doi.org/10.1186/s13662-019-1968-9 [Citations: 11]
  2. A New High Accuracy Off-Step Discretisation for the Solution of 2D Nonlinear Triharmonic Equations

    Singh, Swarn | Singh, Suruchi | Mohanty, R. K.

    East Asian Journal on Applied Mathematics, Vol. 3 (2013), Iss. 3 P.228

    https://doi.org/10.4208/eajam.140713.130813a [Citations: 3]
  3. Optimal Error Estimates of Compact Finite Difference Discretizations for the Schrödinger-Poisson System

    Zhang, Yong

    Communications in Computational Physics, Vol. 13 (2013), Iss. 5 P.1357

    https://doi.org/10.4208/cicp.251011.270412a [Citations: 13]