Matlab code help on Euler's Method

Question

Sanjida Ahmed 2016-4-11

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/278300-matlab-code-help-on-euler-s-method

评论： Ahmed J. Abougarair 2024-3-20

I have to implement for academic purpose a Matlab code on Euler's method(y(i+1) = y(i) + h * f(x(i),y(i))) which has a condition for stopping iteration will be based on given number of x. I am new in Matlab but I have to submit the code so soon. I am facing lots of error in implementing that though I haven't so many knowledge on Matlab. If anyone provide me so easy and simple code on that then it'll be very helpful for me. Thank you.

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Muhammad Tahir 2023-12-24

移动：Dyuman Joshi 2023-12-26

y'=2x-3y+1, y(1)=5, y(1.2)=? MATLAB code using euler'method to obtain a four decimal and h= 0.1

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Answer 1

James Tursa 2016-4-11

12
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/278300-matlab-code-help-on-euler-s-method#answer_217451

在 MATLAB Online 中打开

Here is a general outline for Euler's Method:

% Euler's Method
% Initial conditions and setup
h = (enter your step size here);  % step size
x = (enter the starting value of x here):h:(enter the ending value of x here);  % the range of x
y = zeros(size(x));  % allocate the result y
y(1) = (enter the starting value of y here);  % the initial y value
n = numel(y);  % the number of y values
% The loop to solve the DE
for i=1:n-1
    f = the expression for y' in your DE
    y(i+1) = y(i) + h * f;
end

It is based on this link, which you have already read:

http://www.mathworks.com/matlabcentral/answers/224319-euler-method-without-using-ode-solvers

You need to fill in the values indicated, and also write the code for the f line. What is the DE you are trying to solve?

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ATUL 2023-3-10

how many iterations, we will decide in this?

Ahmed J. Abougarair 2024-3-20

% Euler's Method

% Initial conditions and setup

clc

clear

h = input('Enter your step size here :'); % step size

x = input('Enter the starting value of x :');

xend = input('Enter the ending value of xend :'); % the range of x

n = (xend-x)/h; % the number of y values

y = zeros(1,n); % allocate the result y

y(1) = input('Enter the starting value of y :'); % the initial y value

% The loop to solve the DE

for i=1:n

f(i) = 6- 2*(y(i)/x(i)); % dy/dx = 6-2y/x

y(i+1) = y(i) + h * f(i);

x(i+1)=x(i)+h;

end

[x' y']

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Answer 2

mahmoud mohamed abd el kader 2020-10-27

3
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https://ww2.mathworks.cn/matlabcentral/answers/278300-matlab-code-help-on-euler-s-method#answer_525523

在 MATLAB Online 中打开

h=0.5;
x=0:h:4;
y=zeros(size(x));
y(1)=1;
n=numel(y);
for i = 1:n-1
    dydx= -2*x(i).^3 +12*x(i).^2 -20*x(i)+8.5 ;
    y(i+1) = y(i)+dydx*h ;
    fprintf('="Y"\n\t   %0.01f',y(i));
end
%%fprintf('="Y"\n\t   %0.01f',y);
plot(x,y);
grid on;

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James Tursa 2021-3-3

编辑：James Tursa 2021-3-3

@shireesha myadari Please delete this comment and open up a new question for this.

Ahmed J. Abougarair 2024-3-20

% Euler's Method

% Initial conditions and setup

clc

clear

h = input('Enter your step size here :'); % step size

x = input('Enter the starting value of x :');

xend = input('Enter the ending value of xend :'); % the range of x

n = (xend-x)/h; % the number of y values

y = zeros(1,n); % allocate the result y

y(1) = input('Enter the starting value of y :'); % the initial y value

% The loop to solve the DE

for i=1:n

f(i) = 6- 2*(y(i)/x(i)); % dy/dx = 6-2y/x

y(i+1) = y(i) + h * f(i);

x(i+1)=x(i)+h;

end

[x' y']

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Answer 3

Bakary Badjie 2021-6-14

1
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https://ww2.mathworks.cn/matlabcentral/answers/278300-matlab-code-help-on-euler-s-method#answer_724585

what is the Matlab function that implements Euler’s method

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Chris Horne 2022-3-31

Is the term 'forward Euler' the same as 'Euler' in terms of the algorithm? Here is my method for solving 3 equaitons as a vector:

% This code solves u'(t) = F(t,u(t)) where u(t)= t, cos(t), sin(t)

% using the FORWARD EULER METHOD

% Initial conditions and setup

neqn = 3; % set a number of equations variable

h=input('Enter the step size: ') % step size will effect solution size

t=(0:h:4).';%(starting time value 0):h step size

nt = size(t,1); % size of time array

%(the ending value of t ); % the range of t

% define the function vector, F

F = @(t,u)[t,cos(t),sin(t)]; % define the function 'handle', F

% with hard coded vector functions of time

u = zeros(nt,neqn); % initialize the u vector with zeros

v=input('Enter the intial vector values of 3 components using brackets [u1(0),u2(0),u3(0)]: ')

u(1,:)= v; % the initial u value and the first column

%n=numel(u); % the number of u values

% The loop to solve the ODE (Forward Euler Algorithm)

for i = 1:nt-1

u(i+1,:) = u(i,:) + h*F(t(i),u(i,:)); % Euler's formula for a vector function F

end

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Answer 4

Rakshana 2022-11-13

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/278300-matlab-code-help-on-euler-s-method#answer_1098158

h=0.5; x=0:h:4; y=zeros(size(x)); y(1)=1; n=numel(y); for i = 1:n-1 dydx= -2*x(i).^3 +12*x(i).^2 -20*x(i)+8.5 ; y(i+1) = y(i)+dydx*h ; fprintf('="Y"\n\t %0.01f',y(i)); end %%fprintf('="Y"\n\t %0.01f',y); plot(x,y); grid on;