Five step block method for solving general second order ODEs directly

This paper presents a five point block method of Runge-Kutta type for solving general second order ordinary differential equations (ODEs) using variable step size. The block method is formulated using Lagrange interpolation polynomial. Most ofthe mathematical problems which involve higher order ODEs could be reduced to system of first order equations. The proposed method obtains the numerical solutions directly without reducing to first order systems of ODEs. The method is used to compute the solutions at five points simultaneously in a block by integrating the coefficients over the closest point in the block. The method will be formulated in terms of linear multistep method and it is equivalent to one step method. The stability region and the order of the block method are also studied. The numerical results obtained shows that the proposed method is better compared to existing block methods in terms of accuracy, total steps and execution time.

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