Items tagged with pdsolve

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Hi Maple folks!

I am trying to solve the following PDE in maple:

pde:= diff(c(x,t),t)+c(x,t)*diff(c(x,t),x)=0

bc:=c(x,0)=piecewise(x < 0, 0, x > 0, 1)

I tried the following:

pdsolve({pde,bc}, c(x, 0))

But it gives no solution, i also tried a numeric solution, but i couldn't make it work. Please help.

Thanks! :)

 

Please illustrate the answer on the example of a simple wave equation, for instance.

will give me

which is indeed a solution of the PDE1

will give me

which is not a solution of the PDE2

However, both differential equations are equal, only the arguments are swapped around. Am I doing something wrong, or is this a bug?

Thanks

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Member: faisal http://www.mapleprimes.com/users/faisal
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> restart; with(PDETools), with(plots);
> n := .3; Pr := 7; Da := 0.1e-4; Nb := .1; Nt := .1; tau := 5;
> Eq1 := (1-n)*(diff(f(x, y), `$`(y, 3)))+(1+x*cot(x))*f(x, y)*(diff(f(x, y), `$`(y, 2)))-(diff(f(x, y), y))/Da+(diff(f(x, y), y))^2+n*We*(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), `$`(y, 3)))+sin(x)*(theta(x, y)+phi(x, y))/x = x*((diff(f(x, y), y))*(diff(f(x, y), y, x))+(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), x)));
> Eq2 := (diff(theta(x, y), `$`(y, 2)))/Pr+Nt*(diff(theta(x, y), y))^2/Pr+Nb*(diff(phi(x, y), y))*(diff(theta(x, y), y))/Pr+(1+x*cot(x))*f(x, y)*(diff(theta(x, y), y)) = x*((diff(f(x, y), y))*(diff(theta(x, y), x))+(diff(theta(x, y), y))*(diff(f(x, y), x)));
> Eq3 := Nb*(diff(phi(x, y), `$`(y, 2)))/(tau*Pr)+Nt*(diff(theta(x, y), `$`(y, 2)))/(tau*Pr)+(1+x*cot(x))*f(x, y)*(diff(phi(x, y), y)) = x*((diff(f(x, y), y))*(diff(phi(x, y), x))+(diff(phi(x, y), y))*(diff(f(x, y), x)));
> ValWe := [0, 5, 10];
> bcs := {Nb*(D[2](phi))(x, 0)+Nt*(D[2](theta))(x, 0) = 0, f(0, y) = ((1/12)*y)^2*(6-8*((1/12)*y)+3*((1/12)*y)^2), f(x, 0) = 0, phi(0, y) = -.5*y, phi(x, 12) = 0, theta(0, y) = (1-(1/12)*y)^2, theta(x, 0) = 1, theta(x, 12) = 0, (D[2](f))(x, 0) = Da^(1/2)*(D[2, 2](f))(x, 0)+Da*(D[2, 2, 2](f))(x, 0), (D[2](f))(x, 12) = 0};
> pdsys := {Eq1, Eq2, Eq3}; for i to 3 do We := ValWe[i]; ans[i] := pdsolve(pdsys, bcs, numeric) end do;
> p1 := ans[1]:-plot(theta(x, y), x = 1, color = blue); p2 := ans[2]:-plot(theta(x, y), x = 1, color = green); p3 := ans[3]:-plot(theta(x, y), x = 1, color = black);
> plots[display]({p1, p2, p3});

I have a complicated set of first-order differential equations, which Maple seems capable of solving. So far so good. The obtained solution is fed into another complicated set of first-order differential equations, which, again, Maple seems capable of solving.

But this final (combined) solution cannot possibly be the complete one as it does not contain a specific (sub)solution which DOES satisfy both sets of equations (checked in Maple by evaluating these equations for that specific solution). And there is no warning raised concerning any solutions that may have been lost.

The problem seems to be that the integrational constants associated with solving (in turn) the two sets of equations become messed up together, or erroneously 'reused', in some mysterious way. For if I rename the integration constants of the first solution before feeding it into the second set of equations, then this specific subsolution IS contained in the final solution.

Therefore the following questions:

1.) Could there possibly be some erroneous 'reuse' of integration constants going on? It seems to me that in solving the second set of equations, PDEtools:-Solve would have to make sure that it numbers any new integration constants in such a way that there would be no conflict with the ones obtained in solving the first set of equations.

2.) Is there some (global) variable that determines what letter is assigned for the integration constants? I could use any such to easily switch names between the first and second solving.

PS: I think, it makes little sense to upload any code/worksheet here.

 

I'm trying to solve Laplace's equation in Maple in 2-D domain. But while writing the last line "pdsolve(pdef)" (to get the final solution) and after that hitting enter, it doesn't shows anything. Please help me regaring this.

I am trying to solve the particular system of partial differential equation. But I get the following error.pdsolve.mw
 

"restart;  f(x,y):=x*y:  yy:={diff(f(x,y),x)=0,diff(f(x,y),y)=0}:  ee:=pdsolve(yy,numeric);"

Error, (in pdsolve/numeric) invalid subscript selector

 

``


 

Download pdsolve.mw

 


 

Download example.mw

I tried to solve some linear differential equations,

but the result is incomplete.

The complete solutions have been derived by hand.

How can I get the right result using maple?

The example is from determining symmetres of differential equations.

Thank you!

Consider a standard initial/boundary value problem for the heat equation on the interval x ∈ [0,1]:

restart;
pde := diff(u(x,t),t) = diff(u(x,t),x,x);
ic := u(x,0) = f(x);
bc := u(0,t)=0,  u(1,t)=0;

Then
pdsolve({pde, ic, bc});
produces the expected Fourier series solution.

However, if we change the interval to x ∈ [-1,1], as in:
bc := u(-1,t)=0,  u(1,t)=0;
pdsolve({pde, ic, bc});

then Maple fails to return a solution.  Why?

Dear all

I need a help how can i solve for example the following PDEs with Initial condition and boundary condition given at x=-1, and x=1.

pde:=diff(u(t,x),t)=diff(u(t,x),x$2);

ics:=u(0,x)=sin(x);

Bcs:=diff(u(t,-1),x)=0;

Bcs:=diff(u(t,1),x)=0;

Many thanks

 

 

 

hello...how I can pdsolve three equations with related boundary conditions?

please help me.

thanks...

J := f1(r, z)*f2(r, z)*f3(r, z):

`f&theta;` := f2(r, z)*f3(r, z)/fz:

m0 := 1:

``

g := r*ph/l:

sy := (1/2)*arctan(2*g*fz^2/(-fz^2+g^2+`f&theta;`^2-1)):

I4 := (f2(r, z)^2*cos(sy)^2+f3(r, z)^2*sin(sy)^2-(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2))*cos(b)^2+.5*f2(r, z)*f3(r, z)*(f2(r, z)^2-f3(r, z)^2)*sin(2*sy)*sin(2*b)/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)+((f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)^2+(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2))*sin(b)^2:

I6 := (f2(r, z)^2*cos(sy)^2+f3(r, z)^2*sin(sy)^2-(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2))*cos(b)^2-.5*f2(r, z)*f3(r, z)*(f2(r, z)^2-f3(r, z)^2)*sin(2*sy)*sin(2*b)/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)+((f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)^2+(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2))*sin(b)^2:

L := (I4-1)*exp(K2*(I4-1)^2-1):

N := (I6-1)*exp(K2*(I6-1)^2-1):

P23 := -f2(r, z)*f3(r, z)*sin(b)*cos(b)+(.5*(f2(r, z)^2-f3(r, z)^2))*sin(sy)^2*sin(b)^2:

P32 := -f2(r, z)*f3(r, z)*sin(b)*cos(b)+(.5*(f2(r, z)^2-f3(r, z)^2))*sin(sy)^2*sin(b)^2:

P33 := (f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)*sin(b)^2:

P22 := ((f2(r, z)^2*cos(sy)^2+f3(r, z)^2*sin(sy)^2)^2-(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2)*cos(b)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)-f2(r, z)*f3(r, z)*(f2(r, z)^2-f3(r, z)^2)*sin(2*sy)*sin(b)*cos(b)/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)+(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2*sin(b)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2):

S23 := f2(r, z)*f3(r, z)*sin(b)*cos(b)+(.5*(f2(r, z)^2-f3(r, z)^2))*sin(sy)^2*sin(b)^2:

S32 := f2(r, z)*f3(r, z)*sin(b)*cos(b)+(.5*(f2(r, z)^2-f3(r, z)^2))*sin(sy)^2*sin(b)^2:

S33 := (f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)*sin(b)^2:

S22 := ((f2(r, z)^2*cos(sy)^2+f3(r, z)^2*sin(sy)^2)^2-(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2)*cos(b)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)+f2(r, z)*f3(r, z)*(f2(r, z)^2-f3(r, z)^2)*sin(2*sy)*sin(b)*cos(b)/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2)+(.25*(f2(r, z)^2-f3(r, z)^2))*sin(2*sy)^2*sin(b)^2/(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2):

Trr := k0*(J-1)+(1/3)*m0*(2*f1(r, z)^2-f2(r, z)^2-f3(r, z)^2)/J^(5/3):

`T&theta;&theta;` := k0*(J-1)+m0*(f2(r, z)^2*cos(sy)^2+f3(r, z)^2*sin(sy)^2-(1/3)*f1(r, z)^2-(1/3)*f2(r, z)^2-(1/3)*f3(r, z)^2)/J^(5/3)+2*k1*(L*S22+N*P22)/J:

`T&theta;z` := m0*(f2(r, z)^2-f3(r, z)^2)*sin(sy)*cos(sy)/J^(5/3)+2*k1*(L*S23+N*P23)/J:

`Tz&theta;` := m0*(f2(r, z)^2-f3(r, z)^2)*sin(sy)*cos(sy)/J^(5/3)+2*k1*(L*S23+N*P23)/J:

Tzz := k0*(J-1)+m0*(f2(r, z)^2*sin(sy)^2+f3(r, z)^2*cos(sy)^2-(1/3)*f1(r, z)^2-(1/3)*f2(r, z)^2-(1/3)*f3(r, z)^2)/J^(5/3)+2*k1*(L*S33+N*P33)/J:

`Tr&theta;` := 0:

`T&theta;r` := 0:

Trz := 0:

Tzr := 0:

NULLpartial equations

equ(1) := r*(diff(Trr, r))+Trr-`T&theta;&theta;`:

equ(2) := diff(`T&theta;z`, z):

equ(3) := diff(Tzz, z):

# BOUNDARY CONDITIONS

Trr := proc (ro, z) options operator, arrow; 0 end proc:

int((`T&theta;&theta;`-Trr)/r, r, ri, ro) := 13.3*10^3:

2*Pi*(int(Tzz*r, r, ri, ro))-13.3*Pi*ri^2*10^3

Error, (in int) wrong number (or type) of arguments: invalid options or option values passed to indefinite integration. Unknown options: {ro, .8333333333*f1(r, z)*f2(r, z)}

 

int(`T&theta;z`*r^2, r, ri, ro) := 10:

NULL


 

Download for_site.mw

hello...how I can pdsolve three equation with related boundary conditions?

please help me.

thanks...

for_site.mw

Hi Everybody,

I have a simple question: Does Maple solve systems of partial differential equations with boundary conditions?

Can somebody give me an example? 

I have only found numerical solutions to this kind of systems but no symbolic example.

Thanks a lot for yor help.

 

i want to know the area under a diagram plotted by pdsolve, how can i do that? for example in below , what is the area under p1 diagram?


 

restart:k:=5;

5

(1)

EQ:=diff(u(x,t),t)=k*diff(u(x,t),x$2);

diff(u(x, t), t) = 5*(diff(diff(u(x, t), x), x))

(2)

ibc:=u(0,t)=0,u(1,t)=0, u(x,0) = x;

u(0, t) = 0, u(1, t) = 0, u(x, 0) = x

(3)

sol:=pdsolve({EQ},{ibc},numeric);

_m2021168030176

(4)

p1:=sol:-plot(u,x=0.5,t=0...10,style = line,color = "Blue",legend = "heat Plot",axes=boxed);

 

M:=op(1,op(1,p1));

M := Array(1..201, 1..2, {(1, 1) = .0, (1, 2) = .5, (2, 1) = 0.5e-1, (2, 2) = .2702110502740721, (3, 1) = .1, (3, 2) = -0.176887059080428e-1, (4, 1) = .15, (4, 2) = -0.6515347962762406e-2, (5, 1) = .2, (5, 2) = 0.74109221595503715e-2, (6, 1) = .25, (6, 2) = -0.6178984348254404e-2, (7, 1) = .3, (7, 2) = 0.49645329554988925e-2, (8, 1) = .35, (8, 2) = -0.3948699801548904e-2, (9, 1) = .4, (9, 2) = 0.31161325326115076e-2, (10, 1) = .45, (10, 2) = -0.24369292293079273e-2, (11, 1) = .5, (11, 2) = 0.18845070914387395e-2, (12, 1) = .55, (12, 2) = -0.14366378752131666e-2, (13, 1) = .6, (13, 2) = 0.10748767238662861e-2, (14, 1) = .65, (14, 2) = -0.7839388660633711e-3, (15, 1) = .7, (15, 2) = 0.5511660027174686e-3, (16, 1) = .75, (16, 2) = -0.3660810752890637e-3, (17, 1) = .8, (17, 2) = 0.22001797006812284e-3, (18, 1) = .85, (18, 2) = -0.10581369353881973e-3, (19, 1) = .9, (19, 2) = 0.1755251750102873e-4, (20, 1) = .95, (20, 2) = 0.4964665498398858e-4, (21, 1) = 1.0, (21, 2) = -0.9980698165105276e-4, (22, 1) = 1.05, (22, 2) = 0.1362404856962589e-3, (23, 1) = 1.1, (23, 2) = -0.16167000912668705e-3, (24, 1) = 1.15, (24, 2) = 0.17833050358069153e-3, (25, 1) = 1.2, (25, 2) = -0.18805314257842951e-3, (26, 1) = 1.25, (26, 2) = 0.19233515285281392e-3, (27, 1) = 1.3, (27, 2) = -0.19239777469550633e-3, (28, 1) = 1.35, (28, 2) = 0.18923435555607597e-3, (29, 1) = 1.4, (29, 2) = -0.18365024366673088e-3, (30, 1) = 1.45, (30, 2) = 0.17629586775928352e-3, (31, 1) = 1.5, (31, 2) = -0.16769415545232156e-3, (32, 1) = 1.55, (32, 2) = 0.15826324867687376e-3, (33, 1) = 1.6, (33, 2) = -0.1483353129733858e-3, (34, 1) = 1.65, (34, 2) = 0.1381721031382132e-3, (35, 1) = 1.7, (35, 2) = -0.12797783595325005e-3, (36, 1) = 1.75, (36, 2) = 0.11790982779578369e-3, (37, 1) = 1.8, (37, 2) = -0.10808727763435372e-3, (38, 1) = 1.85, (38, 2) = 0.9859851163881829e-4, (39, 1) = 1.9, (39, 2) = -0.8950695218043435e-4, (40, 1) = 1.95, (40, 2) = 0.8085602954949057e-4, (41, 1) = 2.0, (41, 2) = -0.7267321775920382e-4, (42, 1) = 2.05, (42, 2) = 0.6497334507523223e-4, (43, 1) = 2.1, (43, 2) = -0.5776130436199765e-4, (44, 1) = 2.15, (44, 2) = 0.5103426709812118e-4, (45, 1) = 2.2, (45, 2) = -0.4478348725852213e-4, (46, 1) = 2.25, (46, 2) = 0.3899576658643508e-4, (47, 1) = 2.3, (47, 2) = -0.336546405833609e-4, (48, 1) = 2.35, (48, 2) = 0.28741334410836633e-4, (49, 1) = 2.4, (49, 2) = -0.2423552947809686e-4, (50, 1) = 2.45, (50, 2) = 0.20115974495047912e-4, (51, 1) = 2.5, (51, 2) = -0.16360968960468515e-4, (52, 1) = 2.55, (52, 2) = 0.12948742231058999e-4, (53, 1) = 2.6, (53, 2) = -0.985774731176686e-5, (54, 1) = 2.65, (54, 2) = 0.706688518346671e-5, (55, 1) = 2.7, (55, 2) = -0.4555672725651303e-5, (56, 1) = 2.75, (56, 2) = 0.23043650036730538e-5, (57, 1) = 2.8, (57, 2) = -0.29404079279315267e-6, (58, 1) = 2.85, (58, 2) = -0.14933413612624144e-5, (59, 1) = 2.9, (59, 2) = 0.30749105483557417e-5, (60, 1) = 2.95, (60, 2) = -0.4466869448461453e-5, (61, 1) = 3.0, (61, 2) = 0.5684494809229467e-5, (62, 1) = 3.05, (62, 2) = -0.67421491593684444e-5, (63, 1) = 3.1, (63, 2) = 0.765330108066053e-5, (64, 1) = 3.15, (64, 2) = -0.8430551865031369e-5, (65, 1) = 3.2, (65, 2) = 0.9085666798487518e-5, (66, 1) = 3.25, (66, 2) = -0.9629609655930039e-5, (67, 1) = 3.3, (67, 2) = 0.10072579272402201e-4, (68, 1) = 3.35, (68, 2) = -0.1042404728762369e-4, (69, 1) = 3.4, (69, 2) = 0.1069279635035891e-4, (70, 1) = 3.45, (70, 2) = -0.10886958224421352e-4, (71, 1) = 3.5, (71, 2) = 0.11014051364892259e-4, (72, 1) = 3.55, (72, 2) = -0.11081017636391213e-4, (73, 1) = 3.6, (73, 2) = 0.11094257929051255e-4, (74, 1) = 3.65, (74, 2) = -0.11059666495657345e-4, (75, 1) = 3.7, (75, 2) = 0.109826638880031e-4, (76, 1) = 3.75, (76, 2) = -0.10868228414258878e-4, (77, 1) = 3.8, (77, 2) = 0.10720926073958364e-4, (78, 1) = 3.85, (78, 2) = -0.1054493895470911e-4, (79, 1) = 3.9, (79, 2) = 0.1034409209623252e-4, (80, 1) = 3.95, (80, 2) = -0.10121878843963985e-4, (81, 1) = 4.0, (81, 2) = 0.9881484727059153e-5, (82, 1) = 4.05, (82, 2) = -0.9625809905064345e-5, (83, 1) = 4.1, (83, 2) = 0.9357490234275213e-5, (84, 1) = 4.15, (84, 2) = -0.9078917009490728e-5, (85, 1) = 4.2, (85, 2) = 0.87922554398473e-5, (86, 1) = 4.25, (86, 2) = -0.8499461919063325e-5, (87, 1) = 4.3, (87, 2) = 0.8202300151001906e-5, (88, 1) = 4.35, (88, 2) = -0.7902356191213331e-5, (89, 1) = 4.4, (89, 2) = 0.7601052464222056e-5, (90, 1) = 4.45, (90, 2) = -0.72996608149495766e-5, (91, 1) = 4.5, (91, 2) = 0.699931465092186e-5, (92, 1) = 4.55, (92, 2) = -0.6701020229904285e-5, (93, 1) = 4.6, (93, 2) = 0.6405667145430395e-5, (94, 1) = 4.65, (94, 2) = -0.6114038060383664e-5, (95, 1) = 4.7, (95, 2) = 0.5826817736440689e-5, (96, 1) = 4.75, (96, 2) = -0.5544601404792595e-5, (97, 1) = 4.8, (97, 2) = 0.52679025211894145e-5, (98, 1) = 4.85, (98, 2) = -0.4997159946020307e-5, (99, 1) = 4.9, (99, 2) = 0.47327445878452e-5, (100, 1) = 4.95, (100, 2) = -0.4474965546586055e-5, (101, 1) = 5.0, (101, 2) = 0.4224075790442743e-5, (102, 1) = 5.05, (102, 2) = -0.3980277398539528e-5, (103, 1) = 5.1, (103, 2) = 0.3743726399348483e-5, (104, 1) = 5.15, (104, 2) = -0.35145372330544755e-5, (105, 1) = 5.2, (105, 2) = 0.3292786864253045e-5, (106, 1) = 5.25, (106, 2) = -0.3078518569671755e-5, (107, 1) = 5.3, (107, 2) = 0.28717454240173786e-5, (108, 1) = 5.35, (108, 2) = -0.2672453505531053e-5, (109, 1) = 5.4, (109, 2) = 0.2480604841418905e-5, (110, 1) = 5.45, (110, 2) = -0.22961401119743008e-5, (111, 1) = 5.5, (111, 2) = 0.21189811309571416e-5, (112, 1) = 5.55, (112, 2) = -0.19490331186010634e-5, (113, 1) = 5.6, (113, 2) = 0.17861867825155937e-5, (114, 1) = 5.65, (114, 2) = -0.16303202207033257e-5, (115, 1) = 5.7, (115, 2) = 0.14813006599365237e-5, (116, 1) = 5.75, (116, 2) = -0.13389860418240196e-5, (117, 1) = 5.8, (117, 2) = 0.12032264680435905e-5, (118, 1) = 5.85, (118, 2) = -0.10738655154134225e-5, (119, 1) = 5.9, (119, 2) = 0.9507414307327055e-6, (120, 1) = 5.95, (120, 2) = -0.8336882146176523e-6, (121, 1) = 6.0, (121, 2) = 0.7225366029120385e-6, (122, 1) = 6.05, (122, 2) = -0.6171149536407717e-6, (123, 1) = 6.1, (123, 2) = 0.5172500469062582e-6, (124, 1) = 6.15, (124, 2) = -0.422767804599377e-6, (125, 1) = 6.2, (125, 2) = 0.3334939363034557e-6, (126, 1) = 6.25, (126, 2) = -0.24925451730719557e-6, (127, 1) = 6.3, (127, 2) = 0.1698765042164462e-6, (128, 1) = 6.35, (128, 2) = -0.9518819325289293e-7, (129, 1) = 6.4, (129, 2) = 0.25019625957658297e-7, (130, 1) = 6.45, (130, 2) = 0.4079705332935711e-7, (131, 1) = 6.5, (131, 2) = -0.10242728416703212e-6, (132, 1) = 6.55, (132, 2) = 0.16003381713738053e-6, (133, 1) = 6.6, (133, 2) = -0.21377647792892648e-6, (134, 1) = 6.65, (134, 2) = 0.2638119651684455e-6, (135, 1) = 6.7, (135, 2) = -0.31029367903289395e-6, (136, 1) = 6.75, (136, 2) = 0.3533715778983202e-6, (137, 1) = 6.8, (137, 2) = -0.3931920604894687e-6, (138, 1) = 6.85, (138, 2) = 0.4298978711906126e-6, (139, 1) = 6.9, (139, 2) = -0.4636280263535863e-6, (140, 1) = 6.95, (140, 2) = 0.494517759612214e-6, (141, 1) = 7.0, (141, 2) = -0.5226984843620009e-6, (142, 1) = 7.05, (142, 2) = 0.5482977717131691e-6, (143, 1) = 7.1, (143, 2) = -0.5714393423533197e-6, (144, 1) = 7.15, (144, 2) = 0.5922430708876365e-6, (145, 1) = 7.2, (145, 2) = -0.610825001331253e-6, (146, 1) = 7.25, (146, 2) = 0.6272973725430698e-6, (147, 1) = 7.3, (147, 2) = -0.641768652482882e-6, (148, 1) = 7.35, (148, 2) = 0.6543435802710991e-6, (149, 1) = 7.4, (149, 2) = -0.6651232151103739e-6, (150, 1) = 7.45, (150, 2) = 0.6742049912106031e-6, (151, 1) = 7.5, (151, 2) = -0.6816827779311618e-6, (152, 1) = 7.55, (152, 2) = 0.6876469444194619e-6, (153, 1) = 7.6, (153, 2) = -0.6921844280904861e-6, (154, 1) = 7.65, (154, 2) = 0.6953788063481056e-6, (155, 1) = 7.7, (155, 2) = -0.6973103710014924e-6, (156, 1) = 7.75, (156, 2) = 0.6980562048815929e-6, (157, 1) = 7.8, (157, 2) = -0.6976902602061175e-6, (158, 1) = 7.85, (158, 2) = 0.6962834382846133e-6, (159, 1) = 7.9, (159, 2) = -0.6939036701932665e-6, (160, 1) = 7.95, (160, 2) = 0.690615998086224e-6, (161, 1) = 8.0, (161, 2) = -0.6864826568410622e-6, (162, 1) = 8.05, (162, 2) = 0.6815631557688252e-6, (163, 1) = 8.1, (163, 2) = -0.6759143601450263e-6, (164, 1) = 8.15, (164, 2) = 0.669590572344911e-6, (165, 1) = 8.2, (165, 2) = -0.6626436123890619e-6, (166, 1) = 8.25, (166, 2) = 0.6551228977290213e-6, (167, 1) = 8.3, (167, 2) = -0.647075522119317e-6, (168, 1) = 8.35, (168, 2) = 0.6385463334437125e-6, (169, 1) = 8.4, (169, 2) = -0.629578010378859e-6, (170, 1) = 8.45, (170, 2) = 0.6202111377936157e-6, (171, 1) = 8.5, (171, 2) = -0.6104842807971703e-6, (172, 1) = 8.55, (172, 2) = 0.6004340573606388e-6, (173, 1) = 8.6, (173, 2) = -0.5900952094508935e-6, (174, 1) = 8.65, (174, 2) = 0.5795006726227363e-6, (175, 1) = 8.7, (175, 2) = -0.5686816440282655e-6, (176, 1) = 8.75, (176, 2) = 0.5576676488088356e-6, (177, 1) = 8.8, (177, 2) = -0.5464866048451384e-6, (178, 1) = 8.85, (178, 2) = 0.5351648858455677e-6, (179, 1) = 8.9, (179, 2) = -0.5237273827621483e-6, (180, 1) = 8.95, (180, 2) = 0.5121975635274654e-6, (181, 1) = 9.0, (181, 2) = -0.5005975311119593e-6, (182, 1) = 9.05, (182, 2) = 0.488948079906314e-6, (183, 1) = 9.1, (183, 2) = -0.4772687504359755e-6, (184, 1) = 9.15, (184, 2) = 0.46557788242095225e-6, (185, 1) = 9.2, (185, 2) = -0.45389266619653036e-6, (186, 1) = 9.25, (186, 2) = 0.4422291925122823e-6, (187, 1) = 9.3, (187, 2) = -0.43060250073186364e-6, (188, 1) = 9.35, (188, 2) = 0.4190266254556287e-6, (189, 1) = 9.4, (189, 2) = -0.4075146415927183e-6, (190, 1) = 9.45, (190, 2) = 0.39607870790862633e-6, (191, 1) = 9.5, (191, 2) = -0.38473010907775763e-6, (192, 1) = 9.55, (192, 2) = 0.37347929627010353e-6, (193, 1) = 9.6, (193, 2) = -0.362335926303425e-6, (194, 1) = 9.65, (194, 2) = 0.35130889939221703e-6, (195, 1) = 9.7, (195, 2) = -0.34040639552618525e-6, (196, 1) = 9.75, (196, 2) = 0.3296359095107469e-6, (197, 1) = 9.8, (197, 2) = -0.3190042847032402e-6, (198, 1) = 9.85, (198, 2) = 0.30851774547799635e-6, (199, 1) = 9.9, (199, 2) = -0.29818192845446557e-6, (200, 1) = 9.95, (200, 2) = 0.2880019125209349e-6, (201, 1) = 10.0, (201, 2) = -0.2779822476886622e-6}, datatype = float[8], order = C_order)

(5)

 

 

 

 


 

Download heat_equation_(2).mw

The following is the PDE I need to solve.

(x*y+1)*(diff(h(x, y), y, y, y))+(x+h(x, y))*(diff(h(x, y), y, y))-(diff(h(x, y), y))^2+k(x, y) = 0, (10.*(x*y+1))*(diff(k(x, y), y,y))+(10.*x+h(x,y))*(diff(k(x, y), y))-(diff(h(x, y), y))*k(x, y) = 0

 

This is the original boundary condition:

h(0, y) = f(y), h(x, 0) = 0, k(0, y) = g(y), k(x, 0) = 1, k(x, 25) = 0, (D[2](h))(x, 0) = 0, (D[2](h))(x, 25) = 0

 

After using pdsolve it come out the error:

pdsolve(eval(pde2, P = .1), pdebc4, numeric, [h(x, y), k(x, y)], spacestep = .1)

Error, (in pdsolve/numeric/par_hyp) Incorrect number of initial conditions, expected 0, got 2

 

If I remove one of the boundary condition when x=0, maybe h(0,y)=f(y), then the error will be this:

Error, (in pdsolve/numeric/par_hyp) Incorrect number of initial conditions, expected 0, got 1

 

However if I remove both when x=0, it come out this error:

Error, (in pdsolve/numeric) initial/boundary conditions must be defined at one or two points for each independent variable

 

May I know what is the problem of this equations?

P/S: I know its only differentiate with respect to y and is consider to be an ODE( I need more explantion on this please) and I'm still new to maple. Thanks!!

 

Hello

I solved a complex PDE equation in maple but I can not plot the output.

The manner was like bellow:

PDE := [diff(A(z, t), z)+(1/2)*alpha*A(z, t)+(I*beta[2]*(1/2))*(diff(A(z, t), t, t))-(I*beta[3]*(1/6))*(diff(A(z, t), t, t, t))-I*(GAMMA(omega[0]))(abs(A(z, t))^2*A(z, t)) = 0];
IBC := {(D[2](A))(z, 1), A(0, t) = -sin(2*Pi*t), A(z, 0) = sin(2*Pi*z), (D[2](A))(z, 0) = 2*z};
pds := pdsolve(PDE, IBC, type = numeric, time = t, range = 0 .. 1);
pds:-plot3d(A(z, t)*conjugate(A(z, t)), t = 0 .. 1, z = 0 .. 10, shading = zhue, axes = boxed, labels = ["x", "t", "A(z,t)"], labelfont = [TIMES, ROMAN, 20], orientation = [-120, 40]);

It is solved but there is an error like:

Error, (in pdsolve/numeric/plot3d) unable to compute solution for z>INFO["failtime"]:
unable to store 11.2781250000000+4390.00000040000*I when datatype=float[8]

could you please help me?

what is the problem?

 

 

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