Non-polynomial spline for solution of boundary-value problems in plate deflection theory

Abstract

In this paper a non-polynomial quintic spline function is applied to the numerical solution of a certain fourth-order, two-point boundary-value problem occurring in plate deflection theory. Direct methods of orders two, four, and six have been obtained which lead to five-diagonal linear systems. Boundary formulae of various orders have been developed to retain the bandwidth of the coefficient matrix as five. Convergence analysis of the sixth-order method is given. Numerical results are provided to demonstrate the superiority of our methods.