Dynamic Computation of Runge Kutta Fourth Order Algorithm for First and Second Order Ordinary Differential Equation Using Java

TL;DR

This paper presents a dynamic Java implementation of the Runge-Kutta Fourth Order algorithm for solving first and second order ordinary differential equations, improving efficiency over traditional static methods.

Contribution

It introduces a compiler-based approach to dynamically evaluate inputs and implement the RK4 algorithm for various ODE orders, enhancing computational efficiency.

Findings

Developed a Java software for dynamic ODE solving

Achieved more efficient computation compared to traditional methods

Applicable to first and second order differential equations

Abstract

Differential equations arise in mathematics, physics,medicine, pharmacology, communications, image processing and animation, etc. An Ordinary Differential Equation (ODE) is a differential equation if it involves derivatives with respect to only one independent variable which can be studied from different perspectives, such as: analytical methods, graphical methods and numerical methods. This research paper therefore revises the standard Runge - Kutta fourth order algorithm by using compiler techniques to dynamically evaluate the inputs and implement the algorithm for both first and second order derivatives of the ODE. We have been able to develop and implement the software that can be used to evaluate inputs and compute solutions (approximately and analytically) for the ODE function at a more efficient rate than the traditional method.