# Euler's Method

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Matthew Russell on 10 Jun 2019
Commented: Matthew Russell on 11 Jun 2019
Hello,
New Matlab user here and I am stuck trying to figure out how to set up Euler's Method for the following problem:
𝑦′ =sin(𝑡)∗(1−𝑦) with 𝑦(0)=𝑦0 and 𝑡≥0
The teacher for the class I am taking provided us with the following code to use for Euler's Method. The code has been modified with my most recent attempt to solve the problem above. His template worked fine for the problem listed at the top and several others, but when I changed out the variables for the problem above and I get the error message listed at the bottom. I have tried various ways of inputing the code that I found on YouTube or Google searches and none have been able to help. What am I doing wrong?
%This code solves the differential equation y' = 2x - 3y + 1 with an
%initial condition y(1) = 5. The code uses
%the Euler method, the Improved Euler method, and the Runge-Kutta method.
%The function f(x,y) = 2x - 3y + 1 is evaluated at different points in each
%method.
h = 1/16; %Time Step
a = 0; %Starting x
b = 20; %Ending x
n = 321; %Number of Iterations
x = zeros(n,1);
y = zeros(n,1);
x = linspace(a,b,n)'; %Array of x values where evaluate the function
y(1) = 6; %Initial Condition
for i = 1:n-1
y(i+1) = y(i) + h *((sin(x) * ( 1 - y(i)) ; %Euler's Method
end
[x y] %Table showing x and y values
Error: File: Euler_Method.m Line: 21 Column:
47
Invalid expression. When calling a function
or indexing a variable, use parentheses.
Otherwise, check for mismatched delimiters.

Debasish Samal on 10 Jun 2019
There is a parentheses mismatch in your code for the euler's method.
Replace that line with:
y(i+1) = y(i) + h *(sin(x) * ( 1 - y(i))) ; %Euler's Method

#### 1 Comment

Matthew Russell on 11 Jun 2019
Thank you so much. I had to change sin(x) to sin(x(i)) for it to work, but it worked perfect after that.

Raghunandan V on 10 Jun 2019
Hi,
Simple code error. Check this line
y(i+1) = y(i) + h *((sin(x(i)) * ( 1 - y(i)))) ; %Euler's Method

#### 1 Comment

Matthew Russell on 11 Jun 2019
Thank you!