Article ID Journal Published Year Pages File Type
7216630 Journal of King Saud University - Science 2017 22 Pages PDF
Abstract
The existing hybrid methods for solving ordinary differential equations were only derived using specific off-step points. Thus, this paper proposes a new four-step block method with three generalized off-step points for solving initial value problems of fourth order ordinary differential equations directly. The strategy employed to develop this method is interpolating the basis function at yn+j,j=0(1)3 and collocating the fourth derivative of the basis function at all points within the selected interval. The implementation of this method in a block-by-block fashion can overcome the setbacks of applying starting values and predictors which are created in predictor-corrector approach. The convergence analysis of the developed method is performed and the accuracy of the method is tested on several problems. The numerical results indicate that the new method outperforms the existing ones in terms of errors. In addition, the new method does not require much computation when compared with previous methods.
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Physical Sciences and Engineering Chemistry Chemistry (General)
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