A Functionally-Fitted Block Numerov Method for Solving Second-Order Initial-Value Problems with Oscillatory Solutions

Abstract A functionally-fitted Numerov-type method is developed for the numerical solution of second-order initial-value problems with oscillatory solutions. The basis functions are considered among trigonometric and hyperbolic ones. characteristics studied, particularly, it shown that has a third order convergence general ordinary differential equation, $$y''=f \left( x,y,y' \right) $$ y ′ = f x , , fourth convergent special x,y\right) . Comparison other methods in literature, even higher order, shows good performance proposed method.