Parametric Septic Spline Solution for Some Ordinary Differential Equations Occurring in Plate Deflection Theory

Abstract: In this paper, we have developed parametric septic spline methods, which reduces to ordinary septic spline as the parameter τ → 0 for the numerical solution of fourth order linear and nonlinear two point boundary value problems. Using this spline function a few consistency relations are derived for computing approximations to the solution of the problem. Methods of order two, four and six have been obtained which lead to seven diagonal linear system. Boundary equations for existing orders have been developed and truncation error is obtained. Three numerical illustrations are tabulated to demonstrate the practical usefulness of our methods and comparison is made with known methods.