, firstorder differential equation
: aytg(u); t= fy)
second differential equation
convert
=- ky;my"+ by'+ky=f(t)
Natural phenomenon mathematical model solves
post-processing
- >
-> ->
Validation
->
Force balance
Continuity (mass continuity, etc...)
continuity, valume
->
Force displacement relations/contributive law
->
-
(AJ(u] (B]
- >
=
nxc
nxh nx1
solves
- >
1.
2.
condition
contract
11 10-8 preconditiones
I
so thatthey
->
are
(C)(A)(U) (CTT (B)
=
(D](u] (c] (B)
=
+
properly!
I I
solved preconditiones matrix [C]
10,3
-
13000
- >
huge difference, better ways to solve like pivoting
Post
Processing
->
fi(u) k
=
1.
Boundary condition
2. Initial condition I before solvingsolving!
not after
Validation
->
I should (not violate) nature
2. Validation follow againstmeasurement
, 3. Compare with existing
4. Compatibility to
existing languages
is Equilibrium problems
(ii) Propagation (ex: wave propagation in string (time-varying]]
(iii) Eigen problems (finding eigen functions and eigenvalues]
multiple solutions but
discrete, modes of
string ·im
ODE +
EI
= -
9
PDE-
crde det
·reta)--ai
How to
analyse PDE?
vibration of
de vibrating string
+
propagation
am + a + 0
=
(Laplace equationi
1.
memory allocation ->
space/ and time
Order
+(a) I
2.
3.
degree
order-z, degree-1
4 linearity before solving we
analyse
order to choose particul
n
x(x,y) B(x,y) in
=
+
r(u) 14x(x,y) B(x,y)]
=
+
-
al method appropriate
L(u) thatclass
1x(x,y)
=
B(x,y)
+
for
su:
+y d 0
=
Linearity
ua b
=
+
( yy)u ↓[a+ by 2(a) ((b) +
=
0
+ =
↓Sany = 2 d(u)
->
u
x(x,y) 3(x,y)
=
+
, ( +
y(y) (x(x,y) B(x,y) =
8y+y+y
+
+
0
=
+y +ye +
↓(x(x,y)) (((u,y)) 0 +
=
->
u cx(x,y) =
(En 3ty)n (En yzy) (((n,y)
+
+
au c22
=
= =>
+(5) y
((((x,y))
=
5.
Homogenity ->
non-zero
function
at a*8 e
the
directly giving
Domain, Boundary
->
conditions rates
give the values
-
bisichlet condition/essential forced boundaryatthe
ionos
of derivative Newman condition/natural boundary
-- condition
at the
boundary
PDE O12S) IPDE of order 2x5)
forced BC -
to (s-1) in derivative
natural BC -> s to (25-1) in derivative
Ex = -
1
4th older gives a dirichlet you would require newman condi
***
z(z)=- a -
tion a dirichlet B.C
014) -> s =2 - essential desivatives,
I,
In total, I would need is
boundary conditions
x 0,y 0;x
=
= 0,M/dx 0
=
=
x L, y
=
0
=
Natural derivatives
->
it -
(25-13th
n
2,d
=
=
0
-> no condition
for this
: aytg(u); t= fy)
second differential equation
convert
=- ky;my"+ by'+ky=f(t)
Natural phenomenon mathematical model solves
post-processing
- >
-> ->
Validation
->
Force balance
Continuity (mass continuity, etc...)
continuity, valume
->
Force displacement relations/contributive law
->
-
(AJ(u] (B]
- >
=
nxc
nxh nx1
solves
- >
1.
2.
condition
contract
11 10-8 preconditiones
I
so thatthey
->
are
(C)(A)(U) (CTT (B)
=
(D](u] (c] (B)
=
+
properly!
I I
solved preconditiones matrix [C]
10,3
-
13000
- >
huge difference, better ways to solve like pivoting
Post
Processing
->
fi(u) k
=
1.
Boundary condition
2. Initial condition I before solvingsolving!
not after
Validation
->
I should (not violate) nature
2. Validation follow againstmeasurement
, 3. Compare with existing
4. Compatibility to
existing languages
is Equilibrium problems
(ii) Propagation (ex: wave propagation in string (time-varying]]
(iii) Eigen problems (finding eigen functions and eigenvalues]
multiple solutions but
discrete, modes of
string ·im
ODE +
EI
= -
9
PDE-
crde det
·reta)--ai
How to
analyse PDE?
vibration of
de vibrating string
+
propagation
am + a + 0
=
(Laplace equationi
1.
memory allocation ->
space/ and time
Order
+(a) I
2.
3.
degree
order-z, degree-1
4 linearity before solving we
analyse
order to choose particul
n
x(x,y) B(x,y) in
=
+
r(u) 14x(x,y) B(x,y)]
=
+
-
al method appropriate
L(u) thatclass
1x(x,y)
=
B(x,y)
+
for
su:
+y d 0
=
Linearity
ua b
=
+
( yy)u ↓[a+ by 2(a) ((b) +
=
0
+ =
↓Sany = 2 d(u)
->
u
x(x,y) 3(x,y)
=
+
, ( +
y(y) (x(x,y) B(x,y) =
8y+y+y
+
+
0
=
+y +ye +
↓(x(x,y)) (((u,y)) 0 +
=
->
u cx(x,y) =
(En 3ty)n (En yzy) (((n,y)
+
+
au c22
=
= =>
+(5) y
((((x,y))
=
5.
Homogenity ->
non-zero
function
at a*8 e
the
directly giving
Domain, Boundary
->
conditions rates
give the values
-
bisichlet condition/essential forced boundaryatthe
ionos
of derivative Newman condition/natural boundary
-- condition
at the
boundary
PDE O12S) IPDE of order 2x5)
forced BC -
to (s-1) in derivative
natural BC -> s to (25-1) in derivative
Ex = -
1
4th older gives a dirichlet you would require newman condi
***
z(z)=- a -
tion a dirichlet B.C
014) -> s =2 - essential desivatives,
I,
In total, I would need is
boundary conditions
x 0,y 0;x
=
= 0,M/dx 0
=
=
x L, y
=
0
=
Natural derivatives
->
it -
(25-13th
n
2,d
=
=
0
-> no condition
for this
