# Euler Method – Numerical Differentiation with MATLAB

Euler method is numerical method to solve the first order ordinary differential equation with given initial condition. The Euler method is only first order convergent, i.e., the error of the computed solution is O(h), where h is the time step.

At here, we write the code of Euler Method in MATLAB step by step. MATLAB is easy way to solve complicated problems that are not solve by hand or impossible to solve at page. MATLAB is develop for mathematics, therefore MATLAB is the abbreviation of MATrix LABoratory.

The formula of Euler method is $y_{n+1}=y_{n}+hf(t_{n},y_{n})$

At here, we solve the differential equation $\frac{dy}{dt}=y-t^{2}+1$ by using Euler method with the help of MATLAB.


% Numerical Method
% Euler method using MATLAB coding
% Euler method also known as Runge-Kutta method of order 2
clear all;
close all;
clc;

f=inline('y-t^2+1');
x0=input('Enter x0=');
y0=input('Enter y0=');
xn=input('Enter upper limit of interval xn=');
h=input('Enter width (equal space) h=');
n=(xn-x0)/h;

fprintf('--------------------------------------------\n')
fprintf('    x              y            ynew\n');
fprintf('--------------------------------------------\n')

for i=1:n
y1=y0+h*f(x0,y0);
fprintf('%f      %f       %f \n',x0,y0,y1)
y0=y1;
x0=x0+h;
end