Euler method and Graph

Question

Nasir Holliday 2020-2-22

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/507009-euler-method-and-graph

编辑： Pravin Jagtap 2020-2-25

Hi, I have to solve a an ODE with the Euler method for two separate step sizes and have to place them on same graph. I'm very confused on how to do this... Please help me...

y'=1/y; Initial Condition y(0) = 1;

I have to use Euler method to solve for y(1) for step size deltat = 0.1 and also deltat = 0.01

This is as far as I got and I'm just completely stuck.....

t0=0; t1=1; dt=0.1;  %define time range and step size
y0=1; %initial condition
t=t0:dt:t1; 
y=zeros(size(t,1), size(t,2))
for i=1: ((t1-t0)/dt)
    y(i+1)=y(i)+1/y(i)*dt
end

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Nasir Holliday 2020-2-23

I'm sorry but I'm not really understanding

Walter Roberson 2020-2-23

在 MATLAB Online 中打开

t0=0; t1=1; dt=0.1;  %define time range and step size
y0=1; %initial condition
t=t0:dt:t1; 
y=zeros(size(t));
num_t = length(t);
for i = 1: num_t - 1
    y(i+1)=y(i)+1/y(i)*dt
end

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Answer 1

Pravin Jagtap 2020-2-25

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/507009-euler-method-and-graph#answer_417233

编辑：Pravin Jagtap 2020-2-25

在 MATLAB Online 中打开

Hello Nasir,

Refer to the following function which takes ‘dt’ and ‘y0’ as an input argument and returns the ‘y’ as solution for time vector from 0 to 1 with ‘dt’ as timestep (This is just a demonstrative example. You can modify as per your requirements).

function y = EulerMethod(dt, y0)
    % Preparing the Time vector from tStart to tEnd
    t_Start = 0; 
    t_End = 1;  
    t = t_Start:dt:t_End;
  
    % Initialize the solution vector
    y = zeros(size(t)); 
    % Impose Initial Condition
    y(1) = y0;
    
    % Compute the Solution vector using the Eulers Method
    num_t = length(t);
    for i = 1: num_t - 1
        y(i+1)=y(i)+((1/y(i))*dt);
    end
end

Call the above function for different values of ‘dt’ as follows and plot it

% call the function for dt 0.1
y1 = EulerMethod(0.1,1);
% call the function for dt 0.01
y2 = EulerMethod(0.01,1);
% Plot the corresponding solutions 
t1 = 0:0.1:1;
plot(t1,y1)
hold on
t2  = 0:0.01:1;
plot(t2,y2) 