ABSTRACT
The methods to find exact analytical solutions of ordinary differential equations vary from equation to equation and are dependent on the boundary and initial conditions. It uses the same subroutine RKPC developed originally for solving initial value problems. There are many situations where an exact solution virtually does not exist due to nonlinearity in the differential equation together with complex boundary or initial conditions. A predictor-corrector method employs first a predictor, and the predicted value is then corrected by a corrector that is iterated to convergence, reducing the actual error considerably as compared to the predictor. The open formula itself is sufficient to solve an ordinary differential equation. The fourth-order Runge-Kutta method requires four calculations of the function at each step, whereas any P-C method requires one calculation of the function by the predictor and one evaluation for each iteration by the corrector.
