Single cell Numerov type discretization for 2D biharmonic and triharmonic equations on unequal mesh

Abstract

In this article using nine point single cell, we report difference methods of accuracy of  for the solution of two dimensional multi-harmonic elliptic equations on unequal mesh, where k>0 and h>0 are grid sizes in y- and x-coordinates respectively. In all cases, we use Numerov type discretization. For a fixed value of (k/h²), the proposed methods behave like fourth order in nature. We do not require to discretize the boundary conditions and the values of , n=1,2,… are obtained as by-product of the methods. The resulting matrix system is solved by using the block iterative methods. Comparative results are provided to demonstrate the fourth order behaviour of the proposed methods.