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A fourth order numerical integrator for the solution of second order ODEs
Abstract
A fourth order numerical integrator for direct solution of second order initial value problems in Odes is proposed. This was achieved by obtaining collocation and interpolation equations from the derivative equation and approximate solutions respectively adopting power series as a basis function. These equations were solved for the unknown parameters which were then substituted in the approximate solution to obtain the continuous method. The proposed discrete schemes were obtained by evaluating the continuous scheme at: x = xn+3, xn+2, xn+3/2, and xn+1/2. The method is stable and consistent. Experimental calculation was done with the method to examine its accuracy.
