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>Implicit one-step block hybrid third-derivative method for the direct solution of initial value problems of second-order ordinary differential equations
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Implicit one-step block hybrid third-derivative method for the direct solution of initial value problems of second-order ordinary differential equations
A new one-step block method with generalized three hybrid points for solving initial value problems of second-order ordinary differential equations directly is proposed. In deriving this method, a power series approximate function is interpolated at {xn,xn+r} while its second and third derivatives are collocated at all points {xn,xn+r,xn+s,xn+t,xn+1} in the given interval. The proposed method is then tested on initial value problems of second-order ordinary differential equations solved by other methods previously. The numerical results confirm the superiority of the new method to the existing methods in terms of accuracy.
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