thanx for suggestion my buddy.
u know the orginal problem is a heat equation - one dimensional and time dependent-
T_{xx}+j^{2}=T_{t}
T_{t}=-1/2j\frac{b}{cL}
T(1,t)=0
T(x,0)=0
j,c,b are constant and 0\leqx\leq1
i solved the problem to here:
T(x,t)= j^{2} \sum...
Homework Statement
oh! after trying to re-solve a PDE I reached this:
Homework Equations
\sum\frac{4}{((2n-1)\pi)^2} (a+\frac{4(-1)^{n+1}}{(2n-1)\pi}) cos(\frac{2n-1}{2}\pi x)
n goes feom 1 to \infty and "a" is a constant value.
The Attempt at a Solution
the solution i am...
e^At problem!
1. Homework Statement [/b]
Hi
for given 4 by 4 matrix, say A, find the e^{At}
which t is time variable.
Homework Equations
A= {\left(\begin{array}{cccc} 0 & a & 0 & 0 \\ -a& 0 & 0 & 0\\ 0 & 0 & 0 & a\\0 & 0 & -a & 0 \end{array}\right)t}Y(0).
The Attempt at a...
no! no!
that was not y\dot{}=\left(\begin{array}{cc}-5 & -2 \\ 2 &
-2\end{array}\right) y
this is a second order system of differential equation
y\ddot{}{}=\left(\begin{array}{cc}-5 & -2 \\ 2 &
-2\end{array}\right)y
reducing the order of the system by assuming y\dot{} = p is an idea...
thanx
yes X\dot{} = dX / dt and t is time.
for first-order system of differential equations like:
X\dot{}=AX+BU
the solution is X(t) = e^{At} X(0)+ \int e^{A(t-\tau)} BU(\tau) d\tau
for example I can solve this system : X\dot{} = {0 1 ; 2 3 } X + {0 1} u
but I have problem...
thanx
yes X\dot{} = dX / dt and t is time.
for first-order system of differential equations like:
X\dot{}=AX+BU
the solution is X(t) = e^{At} X(0)+ \int e^{A(t-\tau)} BU(\tau) d\tau
for example I can solve this system : X\dot{} = {0 1 ; 2 3 } X + {0 1} u
but I have problem with...
hi all
this is the general problem
X\ddot{}+AX\dot{}+BX=0
let A, B,X be 2*2 matrices
its application is in vibrations.
any opinion will be great
I can solve the first-order but ...