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 t...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.展开更多
基金This research was supported by’The University of Delhi’under research grant No.Dean(R)/R&D/2010/1311.
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.
