Differential-Equation-Integration-Comparison

Solves ODEs in MATLAB using Euler and RK4 integration, compares them with accurate solutions, and analyzes RMSEs step-by-step.

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Differential Equation Integration Comparison

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Overview

This project compares Euler integration and Runge-Kutta 4th Order (RK4) methods for solving ordinary differential equations in MATLAB. It benchmarks both methods against accurate reference data and an exact solution, then calculates and visualizes RMSEs to show accuracy differences.

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Save Results

• Final RMSEs and computed results are stored in a structured variable answers for easy reference and reporting.

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Key Features

• Implements Euler and RK4 numerical integration
• Compares numerical results with exact and reference solutions
• Interpolates accurate data to align with computed grids
• Calculates and prints RMSEs for each method and step size
• Generates clear comparison plots for Euler, RK4, and exact solutions

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How to Run

• Clone this repository
• Place AccurateDataSP25.mat in the project folder
• Open MATLAB and run the main script
• View generated plots and check the answers structure for final results