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Runge Kutta 4th order ode

version (1.32 KB) by Judah S
solves ode using 4th order Runge Kutta method


Updated 16 Jan 2013

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This code defines an existing function and step size which you can change as per requirement.

P.S: This code has no new feature compared to existing codes available online. Intention behind posting this very simple code is to help students understand the concept and solve assignments.

Cite As

Judah S (2021). Runge Kutta 4th order ode (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (23)

Jay-Jay Masur

Why does it not work for initial conditions y(0) = some number?

Seunghyeon Kim


Yaman Yucel

It does not work for y(0) = 0 initial condition

Nidhi Menon


Great work! What about a code for Runge Kutta method for second order ODE. Something of this nature:
d^2y/dx^2 + 0.6*dy/dx 0.8y = 0

Thank you


Sumith YD

Dogba Djaze

masoud rahmani

Tareque Hossain

how can i solve SIR model using RK4 method in matlab? can you write the code please

faiz islam

sir can you assist me ,that how we can apply 4th order Runge kutta method for 4 coupled equation?
dx/dt=−ax − eω + yz
dy/dt= by + xz
dz/dt= cz + fω − xy
dω/dt = dω – gz
a = 50, b =−16, c = 10, d = 0.2, e = 10, f = 16, g = 0.5
Step size 0.001 .

Ali Abbas

@Shahzaib Asif Very helpful program.JazakAllah

Stephanie Valerio

How do I run/call to this code?

Hamza Fokraoui

for this function : f'''' - f*f''' + 4*g = 0
where i need to insert it in this code?
thank you

Shahzaib Asif

function RK4(f,a,x0,y0,h)

% Runge Kutta Method 4th Order
% function @(x,y) e.g. f=@(x,y)(x+y);
% a = the point up to which you obtain the results
% x0 = initial condition of x
% y0 = initial condition of y
% step size

x = x0:h:a;
y(1) = y0;

for i=1:(length(x)-1)

k1 = f(x(i),y(i));
k2 = f(x(i)+0.5*h,y(i)+0.5*h*k1);
k3 = f((x(i)+0.5*h),(y(i)+0.5*h*k2));
k4 = f((x(i)+h),(y(i)+k3*h));

y(i+1) = y(i) + (1/6)*(k1+2*k2+2*k3+k4)*h;



%Shahzaib Asif (zaibi7402)

Chris K.Y. FUNG

clear coding




Very good to learn. Thanks.


Pi Ting

excellent work


Excellent program,
very helpful.

MATLAB Release Compatibility
Created with R2010a
Compatible with any release
Platform Compatibility
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