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In this article, a power series of order eight is adopted as a basis function to develop one step hybrid block method with three off step points for solving general fourth order ordinary differential equations. The strategy is employed for the developing this method are interpolating the power series at xn and all off-step points and collocating its fourth derivative at all points in the selected interval. The method derived is proven to be consistent, zero stable and convergent with order five. Taylors series is used to supply the starting values for the implementation of the method while the performance of the method is tasted by solving linear and non-linear problems.

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Abstract:In this article, a general two-hybrid one-step implicit third derivative block method is developed for the direct solution of the second order initial value problems through interpolation and collocation approach. To derive this method, the approximate basis function is interpolated at the values {xn, xn+r} while its second and third derivatives are collocated at all points {xn, xn+r, xn+s, xn+1} in the given interval. The new developed method produces better accuracy if compared to the existing methods when solving the same problems.