Numerical Solutions of First and Second Order Ordinary Differential Equations Using the Kth Dimensional Differential Transform Method

This work studies the effect of the kth-order differential transform method to obtain the general solution of initial value problems of ordinary differential equations. The given equation was transformed using the methodologies of the conventional differential transform; the transformed equation was expanded with Taylor series; the resulting terms of the series and the order of the differential equation determines the order of terms in the transformed differential equation to be used.

This approach also provides a closed-form solution; therefore, it is very powerful and effective in finding numerical solutions of first and second order ordinary differential equations. Some numerical examples in first and second order ordinary differential equations were used to ascertain the usability of the method by comparing the numerical method with the analytical solution. The error obtained in the comparison was noticed as negligible. The Method was found to be consistent and accurate; consequently, it is recommended for use for solutions and research purpose.