Implicit Four Step Stormer-cowell-type Method for General Second Order Ordinary Differential Equations

An implicit four step stormer-cowell-typed method for direct solution of general second order ordinary differential equations is proposed in this study. In the derivation of the method, a combination of chebyshev and legendre polynomials was used as basis function to generate system of interpolation and collocation equations at selected grid points to obtain systems of equation. The resulting system of equations was solved for the unknown parameters and the values of these parameters were substituted into the approximate solution of the basis function. The required method was obtained by evaluating and simplify the resulting equations at the last end grid point of the step number. The resulting method is zero-stable, consistent and normalized. Numerical results compared favourably well with the existing methods.