ON THE EULER AND RUNGE-KUTTA METHODS FOR SOLVING FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS
Keywords:
Ordinary differential equations (ODEs), Euler's method, Runge–Kutta method, numerical methods, computational error, programming in DelphiAbstract
This paper presents a comparative analysis of two classical numerical methods for solving first-order ordinary differential equations (ODEs): the Euler method and the fourth-order Runge–Kutta method. The authors provide theoretical justifications for both methods, computational algorithms, and calculation tables for a test problem. The study clearly demonstrates the advantage of the Runge–Kutta method: with the same integration step, the error of this method ($0.0003$) was three orders of magnitude lower than that of the Euler method ($0.3338$). The practical significance of the work is confirmed by the presented software implementation in the Delphi language, which allows for the automation of the ODE solution process.
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