Analytical and numerical solutions of some differential equations: a comparative study using Natural transform and Runge-Kutta method

This paper focuses on Natural transform and the Runge-Kutta numerical method. These techniques have been used to analyze blood glucose concentrations and electrical circuits. These examples have been selected to demonstrate the applicability of Natural transform in many different areas. It was aimed to solve electrical circuits, which are generally solved by Laplace transform in engineering literature, with Natural transform and to obtain a comparative solution with Runge-Kutta method, which is a numerical method. These engineering problems defined with differential equations were analyzed using Natural transform. Firstly, the differential equations were written using the Natural transform, then the new equations were solved and applying the inverse transform, the results of the equations were obtained. The fourth-order Runge-Kutta numerical method was the second method employed in this study. The results found with this methods were presented in tables and compared graphically. The results applying Natural transform and Runge–Kutta method are equivalent to exact solution.