USING QUASI-UNIFORM GRIDS FOR SOLVING THE BIHARMONIC EQUATION WITH DIRICHLET BOUNDARY CONDITIONS IN SEMISTRIP

Abstract

Boundary value problems for biharmonic equations have many applications in physics, mechanics and engineering. In this paper, we find an approximation solution of the biharmonic problem with Dirichlet boundary conditions in a semistrip. Using quasi-uniform grids to find mostly near-finite boundary values and at the same time be able to handle boundary conditions at infinity. Using the idea of Polozhii in the method of summary representations to transform the system of three-point vector equations to systems of three-point scalar equations. Some examples demonstrate the applicability of the proposed method.