Please help me out to solve the following problem:

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')

[Walter Roberson]

This is your 4th copy of the same question. You did not include the actual error message in any of them.

Answer 1

[Walter Roberson]

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])