Convergence of numerical approximations to a fourth order boundary value problem

Abstract

A convergence theorem is obtained for numerical methods applied to the plate deflection boundary value problem. It is shown that if an approximation of O(h^m ) is used at interior points and at least O(h^m-2 )is used at boundary points then the results are O(h^m-4 ) provided certain conditions are satisfied. A sixth order method is described in detail.

Keywords:

• Finite difference method
• lipschitz condition
• plate deflection theory
• positive definite matrix
• symmetric and skew symmetric matrices
• two-point boundary value problem
• tridiagonal matrix

C.R. Categories:

• 5.17

†On leave from the Department of Mathematics, University of Stirling, Scotland.

†On leave from the Department of Mathematics, University of Stirling, Scotland.

Notes

†On leave from the Department of Mathematics, University of Stirling, Scotland.