On solution of two point second order boundary value problems using semi-analytic method

Abstract EN

In this paper a new method is proposed for the solution of two-point 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 oscillatory 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 problems involving nonlinear equations and/or boundary conditions.

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.