Mathematical Modeling

Feb 07, 2026

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This document outlines a comparative analysis of Runge-Kutta (RK) methods applied to two problems: a linear ordinary differential equation (ODE) and a non-linear ODE. Problem 1 involves the implementation of RK methods of order 2 and order 4, with results compared against MATLAB's ODE23 and ODE45 solutions. Problem 2 presents a non-linear case where no exact solution exists, but numerical approaches yield viable results. The study emphasizes the importance of selecting appropriate analytical strategies for different problem types.

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Mathematical Modeling

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Mathematical Modeling Group 6 – 한종환, 위성현, 임학수.
Out Line -RK? merit? -Problem 1 -Problem 2 -Summary
Preliminary We don’t need to calculate difficult derivatives.
Problem 1
Problem 1 MATLAB code Order 4 Order 2
Problem 1 Result of RK 2
Problem 1 Result of RK 4
Problem 1 Result of ODE23 x value y value x value y value
Problem 1 Result of ODE45 x value y value
Problem 1 Exact solution : y = 1/(1-x)
Q&A Q&A
Problem 2 Non-linear : no exact solution.
Problem 2 MATLAB code
Problem 2
Summary - problem 1 : Linearbut cant find answer using numerical approach. It is need to analytic view.- problem 2 : Nonlinear but can find answer using numerical approach.
Q&A Q&A