MATLAB: Help me with this task using (Euler`s method)

eulerMATLAB

Question:

Use this method to solve the following IVP:

A series RC circuit with R = 5 W and C = 0.02 F is connected with a battery of E = 100 V. At t = 0, the voltage across the capacitor is zero.

(a) Obtain the subsequent voltage across the capacitor.

(b)find the true error if the exact solution is: Vc = V(1 – e^(–t/RC))

Hint:

Use the formula

r(dq/dt)+(q/c)=v

———————————————

It is giving me msg operator '*' is not supported for operands of type 'function_handle'

also i wanna ypu give me advices on my work if i working right or wrong to improve as it`s my first time to use matlab

My Work:

R=5;
C=0.02;
E=100;
Y0=0;
Xinitial=0;
Xfinal=1; 
h=0.01;
X=Xinitial:h:Xfinal;
Y = zeros(size(X));
N=(Xfinal-Xinitial)/h;
for i=1:N-1
Ydot=@(t,q) (E-q/C)/R;
Y(i+1) = Y(i) + h*(Ydot);
end
Vreuler= Y0 / C;
Exact=E * (1 - exp(-X/(R*C)));
Error=(Exact-Vreuler)/Exact;
polt(x.y); grid onh

Best Answer

The function handle is something you only need to create once, before the for-loop starts. Then call that function handle with your state inside the loop. E.g.,

Ydot = @(t,q) (E-q/C)/R;
Y(1) = Y0;
for i=1:N-1
    Y(i+1) = Y(i) + h*Ydot(X(i),Y(i));
end

Then the plot would be

plot(X,Y,X,Exact); grid on

And this is a more robust way of defining N:

N = numel(X);

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MATLAB: Help me use this formula to complete this task (Runge–Kutta methods)

First, your derivative function should be obtained from your differential equation, not from the solution as you have it. You were given the following:

r(dq/dt)+(q/c)=v

So first solve this for the derivative (dq/dt):

(dq/dt) = (v - q/c)/r

Now you can use this expression to form a function handle for calculating this derivative given the state q:

v = something  <-- you fill this in
c = something  <-- you fill this in
r = something  <-- you fill this in
Ydot = @(t,q) (v-q/c)/r;  % based on the DE, not on the solution! Make sure you define v, c, r first!

(Side Note: I am using the (t,q) signature because it matches MATLAB syntax, even though your DE doesn't use t)

In your loop, you need to be calling the derivative function with the current state to calculate the derivative at that point. You are only doing this for Y currently, but this would only work for you in cases where the derivative doesn't depend on t. In your particular case this is true, but I would advise setting up your code so that it works regardless.E.g. something like this using X(i) on the rhs:

Y(1) = Y0;
for i=1:N
    K1 = Ydot(X(i)      ,Y(i)         );
    K2 = Ydot(X(i)+0.5*h,Y(i)+0.5*h*K1);
       :
    Y(i+1) = Y(i) + h/6*(K1+2*K2+2*K3+K4);
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Should be like this

>> h = 0.01;
begin = 0.0;
finish = 5;   % Don't use end here as that's a reserved word in MATLAB
x = begin:h:finish;
y = zeros(size(x));
y(1) = 2;
for i=1:numel(y)-1
    f = sin(y(i)).*sin(x(i).^2);  % note that you had .)*  when you should have had ).*  
    y(i+1) = y(i) + h .* f;
end
plot(x,y);
grid on;

Best Answer

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MATLAB: Help me use this formula to complete this task (Runge–Kutta methods)

MATLAB: Dubble sin in first order Differential Equation

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