Please help me out to solve the following problem:
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Muhammad Fahad
on 26 Mar 2016
Answered: Walter Roberson
on 27 Mar 2016
Actually I want to solve the system of two coupled differential equations in MATLAB by using implicit Euler's Method.My teacher suggests me to use the command "fsolve".Here I am providing the MATLAB code that I construct.I know there must be a very stupid error at line 13 but anyways help me to solve this problem:
clear all
clc
f = @(y) [-80.6*y(1)+119.4*y(2); 79.6*y(1)-120.4*y(2)];
h=1/100;
y(:,1)=[1 ; 4];
t(1)=0;
for i =1:2
y(:,i+1)=fsolve(@(z) -z+y(:,i)+h*f(z),[-10 10])
t(i+1)=t(i)+h;
end
plot(t,y(1,:),'b',t,y(2,:),'b')
hold on
ts=0:0.001:1;
ys(1,:)=(3)*exp(-ts)+(-2)*exp(-200*ts);
ys(2,:)=(2)*exp(-ts)+(2)*exp(-200*ts);
plot(ts,ys(1,:),'r',ts,ys(2,:),'g')
1 Comment
Walter Roberson
on 26 Mar 2016
This is your 4th copy of the same question. You did not include the actual error message in any of them.
Accepted Answer
Walter Roberson
on 27 Mar 2016
You have
y(:,i+1)=fsolve(@(z) -z+y(:,i)+h*f(z),[-10 10])
fsolve invokes the function with a row vector, so z will be a row vector. But in -z+y(:,i)+h*f(z), y(:,i) is a column vector and f(z) is a column vector, so you are trying to add a row vector and a column vector.
Probable fix:
y(:,i+1)=fsolve(@(z) -z(:) + y(:,i) + h*f(z), [-10 10])
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