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Hi, everyone!

I need help.

There are a system of 2 pde's: 

diff(Y(x, t), x$2) = exp(-2*x*b)*(A(x, t)-Y(x, t)), diff(A(x, t), t) = exp(-2*x*b)*(Y(x, t)-A(x, t)) 

and initial and boundary conditions: 

A(x, 0) = 0, Y(0, t) = 0.1, (D[1](Y))(0, t) = 0. 

Goal: 
For each b = 0, 0.05, 0.1. 
1)to plot 3-d  Y(x,t): 0<=x<=20,0<=t<=7. 
2)to plot  Y(x,4). 

Are there any methods with no finite-difference mesh?


I realized the  methods such as  pds1 := pdsolve(sys, ibc, numeric, time = t, range = 0 .. 7)  can't help me:

Error, (in pdsolve/numeric/match_PDEs_BCs) cannot handle systems with multiple PDE describing the time dependence of the same dependent variable, or having no time dependence 

I found something, that can solve my system analytically: 
pds := pdsolve(sys), where sys - my system without initial and boundary conditions. At the end of the output: huge monster, consisted of symbols and numbers :) And I couldn't affiliate init-bound conditions to it.

I use Maple 13. 

Is it possible to solve (numerically or symbolically) the system of PDEs
sys:={diff(Y(x, t), x$2) = exp(-2*x*b)*(A(x, t)-Y(x, t)), diff(A(x, t), t) = exp(-2*x*b)*(Y(x, t)-A(x, t)) }
under the conditions
ibc:={A(x, 0) = 0, Y(0, t) = 0.1, D[1](Y)(0, t) = 0},
 where the parameter b takes the values 0,0.05,0.1, in Maple? The ranges are t=0..7, x=0..20.

Hi ,

I would like to resolve the Kortweg and de Devries equation :

> KDV2:= diff( u(X,T), T)+ 6*u(X,T)*diff(u(X,T),X)+ diff(u(X,T),X$3);

 

I used pdsolve but I have a problem to enter the IBC :

I want

u(infinity, t) =0
u( -infinity, t )=0

u ( x, 0 ) = 1


So I did :


> SOL:=pdsolve(diff( u(X,T), T)+ 6*u(X,T)*diff(u(X,T),X)+ diff(u(X,T),X$3)=0,{u(-10, T) = 0, u(10, T) = 0, u(X, 0) =1},numeric,time=T,range=-10..10);

 

But it doesn't work.

( I remplace infinity by 10 because then I want the graphic representation of the solution )

Could you help me please ?  

Hi

I need a temperature distribution inside a barrier during a heating process.
I will be appreciated for any help.

 

wz

How to animete BC using varying temperature in time?  How to obtain animated solution?

restart

Diffusivity coefficent...

a := 0.1e-5:

Thickness of barrier...

L := .2:

Heating curve:
Time in heating curve (in hours form exmaple)...

Time := seq(i, i = 1 .. 10):

Varying temperature in time [K]....

Temp_in_Time := [433.15, 568.15, 703.15, 838.15, 973.15, 1108.15, 1243.15, 1378.15, 1513.15, 1616.15]:

Initial temperature [K]

Tot := 298:

PDE := diff(T(x, t), t) = a*(diff(T(x, t), x, x)):

--->>>

BC1 := {T(0, t) = Temp_in_Time[2], T(L, t) = Temp_in_Time[2], T(x, 0) = Tot}:

sol := pdsolve(PDE, BC1, numeric, timestep = 50):

sol:-plot(t = 3*3600, thickness = 3, colour = red);

 

``



Download heating.mw

restart:

Eq1:=S*diff(f(x,t),x,t)+diff(f(x,t),x)^2-f(x,t)*diff(f(x,t),x$2)=diff(f(x,t),x$3);

BCs := {D[1](f)(0,t)=cos(t), f(0,t)=0,D[1](f)(L,t)=0};

ICs := {f(x,0)=0};

S:=10:L:=5:
smod3:= pdsolve(Eq1,ICs union BCs,numeric,range=0..L);

smod3:-plot(t=0,  color=red):

it seems to me that the problem is due to the mixed bcs. Any way around?

Cheers!

I  get  this  from  pdsolve as a  "solution"

 

p[42] := -Pi+.2+3.0*x+3.2*t+2*Intat(2.25*_f/sqrt(-1.5*_f*(-1.6+4.0500*_f^2+3.7125*_f)), _f = 0)

 

it does not eval to anything, what is this ?

https://drive.google.com/file/d/0B2D69u2pweEvMV92SGhtRGZONFk/edit?usp=sharing

a error and code in this attachment mw

i can pdsolve it, but numeric pdsolve it get error

> sol := pdsolve({ICS, sys1, sys2, sys3, sys4, sys5, sys6, sys7}, numeric, method = rkf45, parameters = [a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p], output = listprocedure);

Error, (in pdsolve) invalid input: `pdsolve/numeric` expects its 2nd argument, IBCs, to be of type {set, list}, but received method = rkf45

 

restart;

x11:=[1.05657970467127, .369307407127487, .400969917393968, .368036162749865, .280389875142339, .280523489139136, .283220960827744, .373941285224253, .378034013792196, .384412762008662, .358678988563716, .350625923673556, .852039817522304, .362240519978640, 1.03197080591829, .343650441408896, .982510654490390, .404544012440991, .422063867224247, 1.20938803285209, .455708586000668, 1.22503869712995, .388259397947667, .472188904769827, 1.31108028794286, 1.19746589728366, .572669348193002];

y11:= [.813920951682113, 10.3546712426210, 2.54581301217449, 10.2617298458172, 3.82022939508992, 3.81119683373741, 3.90918914917183, 10.5831132713329, 10.8700088489538, 11.0218056177585, 10.5857571473115, 9.89034057997145, .271497107157453, 9.77706473740146, 2.23955104698355, 4.16872072216206, .806710906391666, 11.9148193656260, 12.0521411908477, 2.52812993540440, 12.6348841508094, 2.72197067934160, 5.10891266728297, 13.3609183272238, 3.03572692234234, 1.07326033849793, 15.4268962507711];

z11:= [8.93290500985527, 8.96632856524217, 15.8861149154785, 9.16576669760908, 3.20341865536950, 3.11740291181539, 3.22328961317946, 8.71094047480794, 8.60596466961827, 9.15440788281943, 10.2935566768586, 10.5765776143026, 16.3469510439066, 9.36885507010739, 2.20434678689869, 3.88816077008078, 17.9816287534802, 10.1414228793737, 10.7356141216242, 4.00703203725441, 12.0105837616461, 3.77028605914906, 5.01411979976607, 12.7529165152417, 3.66800269682059, 21.2178824031985, 13.9148746721034];

u11 := [5.19, 5.37, 5.56, 5.46, 5.21, 5.55, 5.56, 5.61, 5.91, 5.93, 5.98, 6.28, 6.24, 6.44, 6.58, 6.75, 6.78, 6.81, 7.59, 7.73, 7.75, 7.69, 7.73, 7.79, 7.91, 7.96, 8.05];

u11 := [seq(close3(t+t3), t3=0..26)];

sys1:=Diff(a1(s,t),s) = a*a1(s,t)+ b*a2(s,t)+ c*a3(s,t)+ d*u(t);

sys2:=Diff(a2(s,t),s) = e*a1(s,t)+ f*a2(s,t)+ g*a3(s,t)+ h*u(t);

sys3:=Diff(a3(s,t),s) = i*a1(s,t)+ j*a2(s,t)+ k*a3(s,t)+ l*u(t);

sys4:=Diff(y(t),t) = m*a1(s,t)+n*a2(s,t)+ o*a3(s,t)+ p*u(t);

sys5:= Diff(a1(s,t),t) = a1(s,t);

sys6:= Diff(a2(s,t),t) = a2(s,t);

sys7:= Diff(a3(s,t),t) = a3(s,t);

sol := pdsolve([sys1, sys2, sys3,sys4,sys5,sys6,sys7]);

t2 := [seq(i, i=1..27)];

xt1 := subs(_C1=1,sol[1]); # a1(t)

xt2 := subs(_C1=1,sol[2]); # a2(t)

xt3 := subs(_C1=1,sol[3]); # a3(t)

ut1 := subs(_C1=1,sol[4]); # u(t)

tim := [seq(n, n=1..27)];

N:=nops(tim):

ICS:=a1(1)=x11[1],a2(1)=y11[1],a3(1)=z11[1],u1(1)=u11[1];

sol:=pdsolve({sys1, sys2, sys3,sys4,sys5,sys6,sys7,ICS}, numeric, method=rkf45, parameters=[ a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p],output=listprocedure);

ans(.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003,.003,.003,.003,.003);

ans:=proc(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) sol(parameters=[ a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p]);

add((xt1(tim[i])-x11[i])^2,i=1..N)+add((xt2(tim[i])-y11[i])^2,i=1..N)+add((xt3(tim[i])-z11[i])^2,i=1..N)+add((ut1(tim[i])-u11[i])^2,i=1..N);

end proc;

result1 := Optimization:-Minimize(ans,initialpoint=[.001,.002,.003,.001,.002,.003,.001,.002,.003,.003,.003,.003,.003,.003,.003,.003]);

how to pdsolve this system...

December 27 2013 rit 200

a1 := Diff(x1(s,t),s$2) = a*x1(s,t)+b*x2(s,t)+c*x3(s,t)+d*u(t);
a2 := Diff(x1(s,t),t)=x1(s,t);
b1 := Diff(x2(s,t),s$2) = e*x1(s,t)+f*x2(s,t)+g*x3(s,t)+h*u(t);
b2 := Diff(x2(s,t),t)=x2(s,t);
c1 := Diff(x3(s,t),s$2) = i*x1(s,t)+j*x2(s,t)+k*x3(s,t)+l*u(t);
c2 := Diff(x3(s,t),t)=x3(s,t);
sys := [a1, a2, b1, b2, c1, c2];
sol := pdsolve(sys);

length exceed limit

a1 := Diff(x1(s,t),s$2) = a*x1(s,t)+b*x2(s,t)+c*x3(s,t)+d*u(t);
b1 := Diff(x2(s,t),s$2) = e*x1(s,t)+f*x2(s,t)+g*x3(s,t)+h*u(t);
c1 := Diff(x3(s,t),s$2) = i*x1(s,t)+j*x2(s,t)+k*x3(s,t)+l*u(t);
sys := [a1, b1, c1];
sol := pdsolve(sys);

sol := pdsolve(sys);
[Length of output exceeds limit of 1000000]

Good evening, dear experts. 

I want to solve the system of PDEs, but i get a mistake:

"Error, (in pdsolve/numeric/xprofile) unable to compute solution for t>HFloat(0.0):

solution becomes undefined, problem may be ill posed or method may be ill suited to solution"

How  can I determine the method for pdsolve?
Thanks for answers.


It's my file with the functions:
restart;
alias(X = x(t, tau), Y = y(t, tau));
xt, yt := map(diff, [X, Y], t)[];
xtau, ytau := map(diff, [X, Y], tau)[];
M := (xtau*(-Y+.1*X)+ytau*X)/(xtau^2+ytau^2);
pde1 := xt = -Y+.1*X-xtau*M;
pde2 := yt = -M*ytau+X;

cond := {x(0, tau) = 1, x(t, 0) = 1, y(0, tau) = 1, y(t, 0) = 1};
Sol := pdsolve({pde1, pde2}, cond, numeric, time = t, range = 0 .. 1);
Sol:-value(t = 1);
%;
Error, (in pdsolve/numeric/xprofile) unable to compute solution for t>HFloat(0.0):
solution becomes undefined, problem may be ill posed or method may be ill suited to solution

 

 

PDE.mw

Hi i attach the file that i have problem with.I guess it is not the first problem with datatype=float[8], but i will appreciate if someone could help me with it.

After calling pdsolve i get the answer in the module "structure", i try to plot it and i get :

Error, (in pdsolve/numeric/plot) unable to compute solution for t<HFloat(0.0):
unable to store [.02091392039809]-5.00000000000000 when datatype=float[8]

 

I am not sure how to interpret it and what should i change to make it work.

My PDE is a Bellman equation and my problem is that i actually know only one boundary condition "icond", is there a way to solve it without other conditions?

Thank you

Issue with pdsolve...

October 22 2013 J4James 175

Hi,

While using pdsolve for a coupled system of pdes, the maple results doen't match with the desired ones.

Here is the system

restart:

Eq1:=diff(f(eta,tau),eta$3)+(f(eta,tau)+h(eta,tau))*diff(f(eta,tau),eta$2)-diff(f(eta,tau),eta$1)^2

+(1+epsilon*cos(Pi*tau))*theta(eta,tau)=Omega*diff(f(eta,tau),tau);

Eq2:=diff(h(eta,tau),eta$3)+(f(eta,tau)+h(eta,tau))*diff(h(eta,tau),eta$2)-diff(h(eta,tau),eta$1)^2

+c*(1+epsilon*cos(Pi*tau...

Hello everyone,

I have a system of PDEs

restart:with(PDEtools):with(plots,implicitplot):

Pr:=1:A:=1:lambda:=1:Omega:=1:epsilon:=1:C1:=1:N:=5:b:=1:fw:=1:a:=1:

Eq1:=diff(f(eta,tau),eta,eta,eta)-diff(theta(eta,tau),eta)*diff(f(eta,tau),eta,eta)+

f(eta,tau)*diff(f(eta,tau),eta,eta)-(diff(f(eta,tau),eta))^2-(1+A*(1-theta(eta,tau)))*diff(f(eta,tau),eta)

+lambda*(1+epsilon*cos(Pi*tau))*theta(eta,tau)-Omega*diff(diff(f(eta,tau),tau),eta);

Hi all,

What else could I try if I encounter this error?

Warning:  Incomplete separation.

--------------------------------

 

I read the pdsolve help page, where it says I should have a solution with this warning, but I got nothing but the error.

 

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