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

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Kendrick Lolange
Kendrick Lolange on 14 Jun 2020
Edited: Ameer Hamza on 15 Jun 2020
This question was flagged by John D'Errico
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Ameer Hamza
Ameer Hamza on 14 Jun 2020
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
Kendrick Lolange on 14 Jun 2020
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
Ameer Hamza on 15 Jun 2020
Original Question asked by Kendrick Lolange:
Title: Use eulers Method using matlab with 2 different step sizes. Please show code for both problems.

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Answers (1)

Ameer Hamza
Ameer Hamza on 14 Jun 2020
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:

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Ameer Hamza
Ameer Hamza on 14 Jun 2020
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
Ameer Hamza
Ameer Hamza on 14 Jun 2020
No, these are the solution at x=2 given by Euler Method. To find the error, you will need to solve the equation analytically.

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