Predictor corrector block methods for solving ordinary differential equations - Waeleh, Nazreen (2011)
In this thesis, the predictor corrector block methods are developed for solving first and higher order initial value problems (lVPs) of ordinary differential equations (ODEs). These methods solve higher order ODEs problem directly without reducing to a system of first order ODEs. The derivation of these proposed block methods are based on the numerical integration method and using an interpolation approach which are similar to the Adams method. These developed block methods solve higher order ODE problems directly in a single code using variable step size strategy. In order to gain an efficient and reliable numerical approximation, these developed block methods are implemented in the predictor corrector mode using a simple iteration technique. The proposed block methods compute several numerical solutions simultaneously and the number of solutions to be computed depends on the feature of the block methods. The integration coefficients of the developed block methods formulae arc stored in the code to avoid tedious and repetitive computation. Several tested problems of ODEs are taken into account in the numerical experiments. This is to emphasize the main features of the proposed methods by comparing these direct block methods with the existing methods that solve the higher order ODEs by reducing to a system of first order ODEs. The results obtained showed that the developed block methods managed to produce acceptable results in terms of maximum error and computational time for solving higher order ODEs directly.