| 3 | A Novel Numerical Method of O(h^(4))for Three-Dimensional Non-Linear Triharmonic Equations显示文摘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,δ^(2)u/δn^(2)andδ^(4)u/δn^(4)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 B.N.Mishra | 2012 | Communications in Computational Physics2012，12，10： | 0 |
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