Variable order step size algorithm for solving second order ODEs - Rasedee, Ahmad Fadly Nurullah; Abdul Sathar, Mohamad Hassan; Wong, Tze Ji; Koo, Lee Feng (UPM Press, 2019)
Previous multi step method using a divided diﬀerence formulation for solving higher order ordinary diﬀerential equations (ODEs) requires calculating the integration co-eﬃcients at every step. In the current research, a multi step method in backwards diﬀerence form is established. The backward diﬀerence formulation oﬀers a solution to the tedious calculation of integration coeﬃcients. Rather than calculating inte-gration coeﬃcients at every step change, a backward diﬀerence formulation requires calculating integration coeﬃcients only once in the beginning and if required once more at the end. The proposed method will also be equipped with a variable order step size algorithm to reduce computational cost (calculation time). Both linear and nonlinear second order ODEs will used to validate the accuracy and eﬃciency of the proposed method.