solving a differential equation

Hi everyone,

I have an equation of the form:

C*dx=-G*x+B or G*x + C*dx - B = 0

How can I solve this?

Dimensions of each matrix are

B = 2000 x 1; C = 2000 x 2000; G = 2000 x 2000; we have 5000 timesteps

also the values of certain rows of the matrix x change with an input waveform at each time step...these rows represent an input voltage

Thanks

Feras

Answer 1

[John BG]

G*x + C*dx - B = 0 same as C*x'+G*x-B=0

launch MuPAD

mphandle=mupad

Symbolic toolbox needed.

MuPAD solves your ODE getting the set of functions that satisfy it, regardless of the size of the arrays.

this the general form of the function that satisfies the ODE your proposed. C4 and C5 are additional constants that define a set of functions all complying with your ODE. If you had initial or/and boundary conditions they might help reduce the solutions.

John

[e-mail]

[Feras Al-Saab]

Hi John. thank you. I have initial conditions of x(0) is equal to 0.

Answer 2

[John BG]

G!=0 means the set of functions that MuPAD resturned is B/G-C4/G*exp(-G*t/C)

x(0)=0 : B/G-C4/G*exp(0)=0 C4=B

then solution to your ODE is: B/G-B/G*exp(-G/C*t)

is is a capacitor discharge?

If you find this answer of any help solving your question, would you please click on the thumbs-up vote link above? thanks in advance

John

[e-mail]

[Feras Al-Saab]

Thank you John.

F