A Novel Numerical Method of O(h^(4))for Three-Dimensional Non-Linear Triharmonic Equations  

作　　者：R.K.Mohanty M.K.Jain B.N.Mishra 

机构地区：[1]Department of Mathematics,Faculty of Mathematical Sciences,University of Delhi,Delhi-110007,India [2]Department of Mathematics,Indian Institute of Technology,Hauz Khas,New Delhi-110016,India [3]Department of Mathematics,Utkal University,Vani Vihar,Bhubaneswar-751004,India [4]4076,C/4,Vasant Kunj,New Delhi-110070,India [5]Department of Mathematics,Rajasunakhala College,Nayagarh,Orissa-752065,India

出　　处：《Communications in Computational Physics》2012年第10期1417-1433,共17页计算物理通讯（英文）

基　　金：This research was supported by’The University of Delhi’under research grant No.Dean(R)/R&D/2010/1311.

摘　　要：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.

关 键 词：Finite differences three dimensional non-linear triharmonic equations fourth order compact discretization LAPLACIAN BIHARMONIC maximum absolute errors 

分 类 号：O17[理学—数学]