Write a MATLAB function to compute a numerical solution to the linear, first-ord

Question

Write a MATLAB function to compute a numerical solution to the linear, first-order system of ordinary differential equations dy -3.1z da dz = 0.95y-z dx over the interval from· -0 to x-10 using finite differences. Hard code the bound- ary conditions y(0) 0.5 and 2(0) 0.5 in the script, but request the step size from the user. Does the choice of step size affect the solution? Plot y(x) and z(x). This sys- tem of differential equations models the concentration response of a reactor system with proportional-integral-derivative (PID) control after undergoing a perturbation

Explanation / Answer

syms x y z;
syms y(x);
syms z(x);
ode(x) = diff(y(x),x) == -3.1*z(x);
cond = y(0) == 0.5;
ySol(x) = dsolve(ode,cond)
ode(x) = diff(z(x),x) == 0.95y(x)-z(x)
cond = z(0) == 0.5;
zSol(x) = dsolve(ode,cond)

Use for Z or for Y.

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