Runge-Kutta Method in Python and MATLAB

Name: Runge-Kutta Method in Python and MATLAB
Rating: 4.4 (78 reviews)

From theory to implementation

Created byYarpiz Team, Mostapha Kalami Heris

Last updated 11/2019

English

What you'll learn

Implementation of Runge-Kutta in Python
Implementation of Runge-Kutta in MATLAB
Solving System of Nonlinear Differential Equations
Simulation of a Lotka-Volterra (Predator-Prey) System

Course content

3 sections • 8 lectures • 35m total length

Introduction to Runge-Kutta Method2:41
Learn the Runge-Kutta method, including the fourth-order RK4, to numerically solve nonlinear differential equations with an initial condition, using MATLAB and Python implementations.
The Lotka-Volterra Model3:26

Implementation of Lotka-Volterra System in MATLAB3:09
Implement a Lotka-Volterra prey-predator model in MATLAB by defining a function that returns time derivatives. Use prey and predator populations with parameters to simulate dynamics.
Implementation of RK4 in MATLAB7:25
Implement the fourth-order Runge-Kutta method in MATLAB to solve an initial value problem by constructing a time vector, computing K1–K4, and updating the state to generate the trajectory.
Wrapping things up: Applying solver to model6:44

Implementation of Lotka-Volterra System in Python2:44
Implement the Lotka-Volterra system in Python using the Runge-Kutta method, defining a parameter dictionary, extracting alpha, beta, delta, gamma, and computing time derivatives as a matrix before applying it.
Implementation of RK4 in Python3:47
Implement the RK4 method in Python and MATLAB by building a time vector, initializing the state, computing k1 through k4, and updating the state.
Wrapping things up: Applying solver to model5:47
Define the system parameters and initial state, implement a Runge-Kutta solver in Python and MATLAB, and compare time-series and plots to validate the model.

Requirements

Python and/or MATLAB Programming
Differential Equations

Description

In this video tutorial, the theory of Runge-Kutta Method (RK4) for numerical solution of ordinary differential equations (ODEs), is discussed and then implemented using MATLAB and Python from scratch. As an example, the well-know Lotka-Volterra model (aka. the Predator-Prey model) is numerically simulated and solved using Runge-Kutta 4th order (RK4), in both languages, Python and MATLAB.

Who this course is for:

Applied Math and Science Students
Engineering Students
Anyone Interested in Numerical Computation
Software Engineers and Programmers

Runge-Kutta Method in Python and MATLAB

What you'll learn

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Course content

Introduction2 lectures • 6min

Implementation of RK4 using MATLAB3 lectures • 17min

Implementation of RK4 using Python3 lectures • 12min

Requirements

Description

Who this course is for: