Crafting a predictor-corrector method


We aim to tailor a predictor-corrector method for an oscillatory-type of solution. The derived method consists of a fourth order predictor and corrector pair. The corrector was chosen from the so-called stability triangle which ensures the method’s stability. Methods with small errors were chosen as correctors. These correctors were each paired to the already existing Milne-Simpson’s predictor. The pair with the least error was selected and examined for a simple harmonic oscillator and a damped driven oscillator. The results clearly illustrate the validity of the method for an oscillatory-type of solution since it has reasonably small errors and it was shown to be comparable to the performance of RK4. Our resulting PC4 method has the advantage of less function evaluations, which translates to less error compared to RK4.