On Solution of Special Case of Two Point Second Order Boundary Value Problems By using Semi-Analytic Method

Abstract

In this paper a new method is proposed for the solution of special case of twopoint
second order boundary-value problems( TPBVP ) ,that is we concerned with
constructing polynomial solutions to two point second order boundary value problems
for ordinary differential equation.
A semi-analytic technique using two-point osculatory interpolation with the fit
equal numbers of derivatives at the end points of an interval [0,1] is compared with
conventional methods via a series of examples and is shown to be that seems to
converge faster and more accurately than the conventional methods and generally
superior, particularly for Variations on a problems .
Also we introduce some general observations about control of a residual and
control of the true error and we prove, there is a more useful connection between
scaled residual and true error.