
Graphical Interpretation of the Slopes Used in the Derivation of Classical Fourth Order Runge-Kutta (RK4) Formula
Category:- Journal; Year:- 2022
Discipline:- Mathematics Discipline
School:- Science, Engineering & Technology School
Abstract
Many practical issues in science
and engineering are formulated by ordinary differential equations (ODE) that
require their own numerical solution. There are a variety of numerical
approaches, e.g. the Euler method, the modified Euler method, the Heun’s
method, the Adam-Bashforth method, and so on, that exist in the context of
numerical analysis. Amongst them, the classical fourth order Runge-Kutta (RK4)
technique is the most reliable and most used. The objective of this paper is
twofold. The first goal is to derive the value of different parameters in the
formulation of the fourth order Runge-Kutta method, and the second goal is to
give details of the geometrical interpretation of this method, principally
explaining the role of the increment parameters in the formula. The whole
discussion will facilitate perception of the key mechanism of the Runge-Kutta
method.