A CLASS OF METHODS FOR THE NUMERICAL SOLUTIONS OF 3D MULTI-HARMONIC ELLIPTIC EQUATIONS ON A GRADED MESH

摘要

In this paper, we report new numerical methods of order two and three for the solution of 3D multi-harmonic elliptic equations on a graded mesh. We first develop numerical methods for 3D Poisson equation on a graded mesh, then we extend our methods to solve 3D bi-harmonic and tri-harmonic equations. Numerical methods for (u/n) are also developed, which are quite often of interest in many areas of Science and Engineering. Numerical results demonstrating the usefulness of proposed methods are presented.