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Home  >  Volume 21 (2012)

A Perturbed Runge-Kutta Method for Solution of Second Order Differential Equations by S. A. Agam and P. O. Odion, Volume 21 (July, 2012), pp 323 - 328
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A fourth order Runge-kutta method with a perturbation term  ∈_(n+1) (x) is derived for solving directly general and stiff second order ordinary Differential Equations of the form y" = f(x, y, y'), y(x0) = y0, y'(x0) = y'0. This is a reconstruction and upgrade of the Runge-kutta methods for first order equations. We define a linear transformation T on set of ordered-three tuples. This enables us to generate four function evaluations that are repeatedly and directly used for the solution y_(n+1). The scheme can be used to solve explicit, implicit, stiff, oscillatory or periodic, non-linear second order ODEs very efficiently. Numerical examples are used to compare with other recent methods.

Keywords: Direct, perturbed, linear transformation, explicit, implicit, stiff, non-linear ODEs.