Use eulers Method using matlab with 2 different step sizes. Please show code for both problems.

[madhan ravi]

What did you try? Paste what you have tried.

[Kendrick Lolange]

I've just been looking up scripts and plugging in my dy/dx but nothing works.

[Kendrick Lolange]

[Kendrick Lolange]

[Ameer Hamza]

How are you calling the function 'euler'? Also, It is better to attach code as text instead of an image. We cannot edit the code using an image.

[Kendrick Lolange]

function euler(func,y0,delt,tf)
t=0:delt:tf;
y(1)=y0;
for i = 1:length(t)-1
    y(i+1)=y(i)+delt*(feval(func,t(i)));
end 
plot (t,y);
xlabel('time')
ylabel('y')
disp(y(end))

[Ameer Hamza]

Original Question asked by Kendrick Lolange:

Title: Use eulers Method using matlab with 2 different step sizes. Please show code for both problems.

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Ameer Hamza]

Since this is a homework question, I will not give a complete code. However, I will point you to resources that can help you to understand how to implement the Euler method in MATLAB.

You can download the zip file given in this answer: https://www.mathworks.com/matlabcentral/answers/98293-is-there-a-fixed-step-ordinary-differential-equation-ode-solver-in-matlab-8-0-r2012b#answer_107643 and study the code of ode1.m. It is the implementation of the Euler method provided in very early releases of MATLAB. It is no longer included in MATLAB, but it is still useful to understand the implementation of the Euler method.

Following FEX packages are also helpful to learn about Euler method and its implementation MATLAB:

https://www.mathworks.com/matlabcentral/fileexchange/31426-euler-method-based-1st-order-ode-solving

https://www.mathworks.com/matlabcentral/fileexchange/45664-euler-method

https://www.mathworks.com/matlabcentral/fileexchange/72522-euler-method

[Kendrick Lolange]

This isn't a homework problem its just review for a quiz please show code.

[Ameer Hamza]

Following code shows how to solve the two equations in you question. Study this code

figure;
euler(@fcn1, 1, 0.1, 2) % h=0.1
title('y''(x)=2*x*y  h=0.1');

figure;
euler(@fcn1, 1, 0.05, 2) % h=0.05
title('y''(x)=2*x*y  h=0.05');

figure;
euler(@fcn2, 1, 0.1, 2) % h=0.1
title('y''(x)=(x-y)/(x+2y)  h=0.05');

figure;
euler(@fcn2, 1, 0.05, 2) % h=0.05
title('y''(x)=(x-y)/(x+2y)  h=0.05');

function euler(func,y0,delt,tf)
t=0:delt:tf;
y(1)=y0;
for i = 1:length(t)-1
    y(i+1)=y(i)+delt*func(t(i), y(i));
end 
plot (t,y);
xlabel('time')
ylabel('y')
disp(y(end))
end

function dy = fcn1(x, y)
    dy = 2*x*y;
end

function dy = fcn2(x, y)
    dy = (x-y)./(x+2*y);
end

[Kendrick Lolange]

Thank you! These are the errors correct?

29.4986

39.0930

0.9769

0.9886

[Ameer Hamza]

No, these are the solution at x=2 given by Euler Method. To find the error, you will need to solve the equation analytically.