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On fourth order boundary value problems arising in beam analysis

Iterative methods for a fourth order boundary value problem

Solution of sixth order boundary value problems using non-polynomial spline technique

Septic spline solutions of sixth-order boundary value problems

Sextic spline solutions of fifth order boundary value problems

In this paper we develop numerical techniques of order 2, 4 and 6 for the solution of a fourth order linear equation. A priori error bound is obtained for the fourth order method to prove the convergence of the finite difference scheme. A suf- ficient condition guaranteeing the uniqueness of the solution of the boundary value problem is also given. Numerical illustrations are tabulated and results compared with the classical Runge-Kutta method. 1. Introduction. We consider the problem of bending a rectangular clamped beam of length / resting on an elastic foundation. The vertical deflection w of the beam satis- fies the system

/pdf/discrete-variable-methods-for-a-boundary-value-problem-with-206aonnceu.pdf

Riaz A. Usmani

Papers

Discrete variable methods for a boundary value problem with engineering applications