Study of Numerical Solutions of Stiff Differential Equations Using Rk Method and Adaptive Stepsize Control Method

Abstract

In this paper, chemical kinetics, electrical circuits, and spring-damping systems, stiff differential equations are specialized initial value issues. Numerical methods are needed for accurate computations because most practical stiff systems lack analytical solutions because to their complexity. This work investigates stiffness phenomena and general-purpose techniques to solve stiff differential equations. We examine numerous standard methods, including the Runge-Kutta method, the Adaptive Stepsize Control for Runge-Kutta method, and the EPISODE ODE Solver package, and list their attributes and computing efficiency. Traditional numerical methods like Euler, explicit Runge-Kutta, and Adams-Moulton require minuscule step sizes for great precision. This may cause substantial round-off errors and solution instability. We analyze the efficiency of the Runge-Kutta and EPISODE algorithms' Adaptive Stepsize Control algorithm to overcome these concerns. Comparative evaluations against accurate solutions demonstrate the effectiveness and dependability of these sophisticated approaches to stiff differential equations.