Fourth-Order Runge-Kutta Algorithm Implementation

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Resource Overview

Implementation of ordinary and partial differential equation solvers using fourth-order Runge-Kutta method with MATLAB GUI interface. Key features include: GUI development, ODE/PDE solvers, difference methods, numerical integration algorithms (Runge-Kutta, Euler, Heun). MATLAB version: 7.0 (R14) with code examples demonstrating algorithm implementation and numerical method comparisons.

Detailed Documentation

This article presents the implementation of fourth-order Runge-Kutta algorithm along with MATLAB-based solvers for ordinary differential equations (ODEs) and partial differential equations (PDEs), featuring a graphical user interface. The implementation includes numerical methods such as difference methods, Runge-Kutta integration, Euler method, and Heun's method. The code structure demonstrates how to handle various differential equation types through MATLAB's numerical computing capabilities. Key implementation aspects include: adaptive step-size control for the Runge-Kutta method, matrix operations for PDE discretization, and callback functions for GUI interactions. The development environment utilized MATLAB version 7.0 (R14), with specific attention to numerical stability and computational efficiency in the algorithm design.

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