Numerical solution of estimating time of death by Newton's Law of Cooling model / Nor Sakinah Kefni, Syafiqah Nasuha Sharif and Kamilia Eliyana Puasa

Forensic science is an application of science to criminal and civil laws. In forensic science, one of the most important issues is to estimate the time of death (TOD) especially during suicide, murder or suspicious death cases. Newton's Law of Cooling model has been widely used to estimate the time of death. In estimating the time of death, Newton's Law of Cooling model is solved analytically and numerically. Numerical method is a complete and specific set of procedures that is used to solve Newton's Law of Cooling model. In this study, there are two different murder cases to be considered in predicting the time of death and the method of solving for this problem are Euler method and Runge-Kutta 4th Order. We solved analytically by separable and numerically by Euler method and Runge-Kutta 4th Order. Next, by identifying the problem and solving the model analytically and numerically, the time of death is predicted. The results are obtained by using the MATLAB software and it is displayed graphically. The range for the solution of estimating time of death for Case 1 is in between 9.40 pm and 9.45 pm while for Case 2 the solutions range are from 10.00 pm to 10.05 pm. Based on relative error, it can be concluded that Runge¬ Kutta 4th Order has better estimation for both cases compare to Euler method since it gives smaller error than Euler method. For further study, other numerical methods such as Adam Bashforth Method, Runge-Kutta Fehlberg Method and Finite Difference Method can also be used in order to get better estimation time of death.