MATLAB: Array indexing multiple equations

differential equationsmultiple state variables

x1(i+1)=x1(i)+x2(i);
x3(i+1)=x3(i)+x4(i);
x5(i+1)=x5(i)+x6(i);
x2(i+1)=x2(i)+cos(x3(i))*x4(i+1)-x6(i+1);
x4(i+1)=x4(i);
x6(i+1)=x6(i)+cos(x5(i))*x2(i+1);

I came up with 6 equations for 6 variables. I have the equations above. x2(i+1) depends on x4(i+1) but that value is not calculated until x2(i+1) is calculated. How do I solve this problem do I need more equations?

Best Answer

You need to do some algebra on these equations before you solve them.

The variable x4 is a constant (x4(i+1) = x4(i) tells us this), so replace x4(i+1) -> x4(i) in the equation for x2(i+1) to give:

x2(i+1)=x2(i)+cos(x3(i))*x4(i)-x6(i+1);  (*)

Now substitute x6(i+1)=x6(i)+cos(x5(i))*x2(i+1) into this equation (*) and solve for x2(i+1). This will give:

x2(i+1)=( x2(i)+cos(x3(i))*x4(i)-x6(i) )/( 1+cos(x5(i)) );

Finally, substitute x2(i+1)=( x2(i)+cos(x3(i))*x4(i)-x6(i) )/( 1+cos(x5(i)) ) into the equation for x6(i+1) to give

x6(i+1)=x6(i)+cos(x5(i))*( x2(i)+cos(x3(i))*x4(i)-x6(i) )/( 1+cos(x5(i)) );

Now you should be okay to solve this problem within a for-loop provided you have a known initial condition.

Related Solutions

MATLAB: FSOLVE requires all values returned by functions to be of data type double.

If you want to solve a system of equations symbolically or using symbolic variables, use the solve function instead of fsolve. The fsolve function requires that the output of the function you specify as the first input be double precision numbers, not symbolic expressions.

If you must use fsolve with symbolic variables inside the function, you must convert those symbolic expressions into numbers using double before returning the numbers (not the symbolic expressions) from the function.

As a very simple example, put all this code into a function example373677.m and run it:

function y = example373677
y = fsolve(@mysubfun, 3);
 
function z = mysubfun(q)
x = sym('x');
r = x.^3-2*x-5;
z = double(subs(r, q));

Of course, with solve this is easier.

syms x
y = solve(x.^3-2*x-5)

You may need to use vpa to approximate y numerically.

vpa(y)

One of the solutions returned in y should match the result you received from running the function.

MATLAB: Subscripted assignment dimension mismatch when cal back the function

basisfunction1 returns a 3-D array R1. Now in

Rl(:,:,j) = basisfunction1(j,N);

you're trying to stick a 3-D array into one plane of the R1 array. You can only put a 2-D image into the j'th plane, not a 3-D image.

Best Answer

Related Solutions

MATLAB: FSOLVE requires all values returned by functions to be of data type double.

MATLAB: Subscripted assignment dimension mismatch when cal back the function

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