Functionally Fitted Block Method for Solving the General Oscillatory Second‐Order Initial Value Problems and Hyperbolic Partial Differential Equations

We present a block hybrid functionally fitted Runge–Kutta–Nyström method (BHFNM) which is dependent on the stepsize and a fixed frequency. Since the method is implemented in a block‐by‐block fashion, the method does not require starting values and predictors inherent to other predictor‐corrector methods. Upon deriving our method, stability is illustrated, and it is used to numerically solve the general second‐order initial value problems as well as hyperbolic partial differential equations. In doing so, we demonstrate the method’s relative accuracy and efficiency.