Investigation of the Estimation Accuracy of 5 Different Numerical ODE Solvers on 3 Case Studies

TL;DR

This study compares five numerical ODE solvers across three case studies, highlighting their varying accuracy and suitability for different dynamic systems in engineering applications.

Contribution

It provides a comparative analysis of five popular ODE solvers on diverse case studies, revealing their strengths and limitations in practical scenarios.

Findings

All solvers perform similarly for logistic population change.

Midpoint method shows better accuracy for temperature change.

None of the solvers accurately estimate market equilibrium price.

Abstract

Numerical ordinary differential equation (ODE) solvers are indispensable tools in various engineering domains, enabling the simulation and analysis of dynamic systems. In this work, we utilize 5 different numerical ODE solvers namely: Euler's method, Heun's method, Midpoint Method, Runge-kutta 4th order and ODE45 method in order to discover the answer of three wellknown case studies and compare their results by calculation of relative errors. To check for the validity of the estimations, the experimental data of previous literature have been compared with the data in this paper which shows a good accordance. We observe that for each of the case studies based on the behavior of the model, the estimation accuracy of the solvers is different. For the logistic population change as the first case study, the results of all solvers are so close to each other that only their solution cost can be considered for their superiority. For temperature change of a building as the second case study we see that in some especial areas the accuracy of the solvers is different and in general Midpoint ODE solver shows better results. As the last case study, market equilibrium price shows that none of the numerical ODE solvers can estimate its behavior which is due to its sudden changing nature.