Explore MATLAB source code curated for "常微分方程" with clean implementations, documentation, and examples.
An efficient numerical implementation of the 4th-order Runge-Kutta method for solving ODEs, featuring code structure explanation and practical application guidance for differential equation problems.
The fourth-order Adams explicit formula offers an efficient numerical method for solving initial value problems in ordinary differential equations, with implementation involving multi-step iteration and predictor-corrector algorithms.
Applying difference equations and numerical differentiation to solve basic practical problems. Experiment 3: Interpolation and Numerical Integration - Problem formulation and solution approaches for interpolation - Principles, advantages, and limitations of Lagrange interpolation - Fundamentals, strengths, and weaknesses of piecewise linear and cubic spline interpolation - MATLAB implementation techniques for piecewise linear and cubic spline interpolation (using functions like interp1 and spline) - Theory and MATLAB coding for trapezoidal and Simpson's integration rules - Error analysis of numerical integration formulas: convergence order concepts - Gaussian quadrature formulas - Generalized integrals and multiple integrals - Applying interpolation and numerical integration to solve real-world problems. Experiment 4: Numerical Solutions of Ordinary Differential Equations - Euler method principles and Runge-Kutta method approaches - Concepts of local truncation error and precision - Runge-Kutta implementations in MATLAB
This MATLAB-based program provides practical examples of interpolation analysis and numerical solution of ordinary differential equations using Euler's method, featuring polynomial interpolation, spline interpolation, and enhanced Euler variants with code implementation details.
MATLAB Algorithm Collection - Solving Initial Value Problems for ODEs with Implementation Examples
System of three-variable ordinary differential equations with dual y-axis graphical visualization
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.
MATLAB Dynamical Systems and Time Series Analysis Toolbox: This comprehensive toolbox enables analysis of dynamical systems and time series data, supporting customization for Ordinary Differential Equations (ODE) and Stochastic Differential Equations (SDE). All analytical methods are encapsulated within modular functions accessible via command-line interface or graphical user interface (GUI). Key functionalities include: ODE/SDE solvers, map integration for time series analysis, filtering techniques, normalization/standardization procedures, histogram/2D histogram visualization, Auto-Correlation Function (ACF), Mutual Information Index (MAI), Fast Fourier Transform (FFT), maximum Lyapunov exponent calculation, and pattern recognition algorithms. Dynamical system analysis features comprise Poincaré section generation, bifurcation diagram plotting, and Lyapunov exponent computation routines.
This function describes the mathematical model of the Apollo satellite and can be directly applied for numerical solutions of ordinary differential equations. The implementation includes key differential equations governing orbital mechanics, with parameters for gravitational effects and satellite dynamics.
This classic boundary value problem case study demonstrates the implementation of compact difference schemes for solving ordinary differential equations, highlighting key computational techniques and algorithm design considerations.