A FAMILY OF K-STEP TRIGONOMETRICALLY-FITTED BLOCK FALKNER METHODS FOR SOLVING SECOND-ORDER INITIAL-VALUE PROBLEMS WITH OSCILLATING SOLUTIONS

A family of K-step Trigonometrically-fitted Block Falkner Methods is considered for the direct solution second order Oscillatory Initial value problems. As unique to methods, two main formulas (one method and one derivative) each k-step some additional formulas. This shall be adapted general oscillatory ordinary differential equations via multistep collocation technique. The idea employed in this study generalized technique based on fitting functions that are combination trigonometric algebraic polynomials, which then implemented a block mode get approximations at all grid points simultaneously. other there no need procedures provide starting values, thus methods selfstarting (sharing advantage Runge-kutta methods). properties proposed reveals they consistent zero-stable, thus, convergent. Furthermore, stability analysis conditions established. evident from numerical results, efficient accurate when compared with recent literature.