KTH Course: Applied Numerical methods Team members
Professor: Lennart Edsberg Andreas Angelou
Paul Evans
Vasileios Papadimitriou
Daniel Tepic
Dionysios Zelios
I.C : ( ,0) 0u x ( ,0) 0u
xt
0 x l
0 x l
B.C : X=0
X=L
2 2
2 2
1u R u u
t L dt LC x
1( , ) ( , ) 0
u ul t l t
t xLC
0 ( ) 1u t [V]
0.004[ ]R 610 [ ]L H 80.25 10 [ ]C F
(N+1) grid-points
Discretization of x-axis into N intervals:
Finite Difference Method
first and second order derivatives:
Central difference approximations
Approximation of the right end of B.C:
Upwind discretization (FTBS)
1 1 1 1
1 1
2 2
2 21
2
n n n n n n n n
i i i i i i i iR
t L t LC x
u u u u u u u u
1
1 1
1( 2 ( 1) )
1
n n n n
i i i i
a
au u u u
2
2
1 ( )
( )
ta
LC x
2
t R
L
65 10t s
N=100 grid-points
N=100 grid-points
N=100 grid-points
N=100 grid-points
62.5 10t s
N=200 grid-points
N=200 grid-points
N=200 grid-points
N=200 grid-points
Taylor expansion
N=100-
N=200
Greater interval for finding stability
Without Taylor expansion
N=100-
N=200
Experimental values
N=100-
N=200
Approximation method stability max
N=100
N=200
65.025 10t 62.506 10t
67.0711 10t 63.5355 10t
64.9962 10t 62.4991 10t
65 10t 62.5 10t
N=100 grid-points
N=100 grid-points
