A Solving Newton’s Law of Cooling Model using Euler Method, Fourth Order Runge-Kutta Method and Fourth Order Implicit Multistep Method

Abstract

This paper discusses the numerical solution of first-order linear ordinary differential equations (ODE’s) of newton’s Law of Cooling. Newton’s law of cooling(NLOC) stated that the rate of heat exchange between an object and its environment is proportional to the temperature difference between the object and the environment. Three proposed methods have been used in this discussion are Euler method, Fourth order Runge-Kutta method(4RKM) and fourth order implicit multistep method(4IMM).This research were done because analytic solution was hard to use for complex problems and results that unable to obtain from analytical method. The differential equation is solved using MATLAB and the results obtained were compared to obtained the most accurate method. This research approximation methods use varying step sizes to compared with the exact solution. Two step sizes are chosen which are 0.1 and 0.05. The three numerical method have been compared numerically and illustrated graphically. It was observed that fourth order runge-Kutta method was the most accurate method in solving Newton’s Law of Cooling