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I am trying to solve a PDE which is converted to ODE when we assign one of the  variables some value. The boundary conditions given to the PDE are numerical values given for fixed numerical values to the two independent variables. I am trying to solve the PDE with the staandard syntax:

pds := pdsolve(pde,[ibc],numeric,time=z,range=0..beta);

The error message I get is:  

Error, (in pdsolve/numeric/process_PDEs) PDEs can only contain dependent variables with direct dependence on the independent variables of the problem, got {theta(z, 0)}

The pde and boundary conditions are as follows:

PDE:   pde := diff(theta(z, 0), z, z)+theta(z, 0)

Where zero is the fixed value for an independent variable

Boundary Condition:  ibc:={theta(0,0)=beta,D[1](theta)(0,0)=0};

When I try to solve it as an ODE the error is:

Error, (in dsolve) not an ODE system, please try pdsolve


Hi everyone,

I am trying to solve the equation of heat tranfer, time dependent, with particular Initial and boundary conditions but I am stuck by technical problems both in getting an analytical solution and a numerical one.

The equation

the equation.

I defined a and b numerically. domain is : and I defined surf_power numerically.

The initial condition is : , T0 defined numerically

The boundary condition is : , because it has a shperical symetry.

To me, it looks like a well posed problem. Does it look fine ?

Problem in analytical solution :

It doesn't accept the boundary condition so I only input the initial condition and it actually gives me back an expression that can be evaluated but it never does : I can't reduce it more than an expression of fourier which I can't eval. The solution :
The solution calculated in (0,0). I was hoping T0...

Are you familiar with these problems ? What would be the perfect syntax you would use to solve this ?

The numerical solution problems :

Sometimes it tells me that my boundary condition is equivalent  to 0 = 0, and I don't see why. Some other times it tells me I only gave 1 boundary/initial condition even if I wrote both. Here is what I wrote for example :

(because it kept asking me to add these two options : 'time' and 'range')

Are you familiar with these problems ? What would be the perfect syntax you would use to solve this ? I must at least have syntax problems because even if I keep reading the Help, it's been a long time since I used Maple.

Thank very much for any indication you could give me !


Hi everyone.

I have been experiencing a problem trying to solve a coupled system of 3 differencial equations

My problem is that a got a message back as I try to solve the system:

"Error, (in pdsolve/numeric/process_IBCs) improper op or subscript selector"

by apply this point that ''all dependent variables must be functions of the same independent variables''

i again accost with another error ''

Error, (in pdsolve/numeric/process_IBCs) initial/boundary conditions can only contain derivatives which are normal to the boundary, got (D[1, 1](w))(x, -3/400000000)


please help me.....very very thanks

I am considering the following PDE and I am getting an error, please suggest a better numerical method than the default one used in maple:


the PDE is:

u_{xx}u^3 - sin(xt)u_{tt} = u(x,t)

u(x, 0) = sin(x), (D[2](u))(x, 0) = cos(x), u(0, t) = cos(t), (D[1](u))(0, t) = sin(t)

Please suggest me a method that will also work for the following PDEs:

u^m* u_{xx} - sin(xt)u_{tt} = u^n

for m,n =0,1,2,3,... for the cases m=n and m not equal n

Here's the code:


pde := u(x, t)^3*(diff(u(x, t), x, x))-sin(x*t)*(diff(u(x, t), t, t)) = u(x, t);

u(x, t)^3*(diff(diff(u(x, t), x), x))-sin(x*t)*(diff(diff(u(x, t), t), t)) = u(x, t)


ibc := u(x, 0) = sin(x), (D[2](u))(x, 0) = cos(x), u(0, t) = cos(t), (D[1](u))(0, t) = sin(t);

u(x, 0) = sin(x), (D[2](u))(x, 0) = cos(x), u(0, t) = cos(t), (D[1](u))(0, t) = sin(t)


pds := pdsolve(pde, [ibc], numeric, time = t, range = 0 .. 1, spacestep = 0.1e-1)

module () local INFO; export plot, plot3d, animate, value, settings; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; end module


pds:-plot3d(u(x, t), t = 0 .. 1, x = 0 .. 1, labels = [t, x, u(x, t)], labelfont = [times, bold, 20], axesfont = [times, bold, 16])

Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.0):
Newton iteration is not converging





I have the following PDE:


u_xx = u_tt + (2^{1/2}u_x-u)^{1/2}


Do you have a proposed algorithm to solve in maple for this PDE? I mean pdsolve won't solve it because it's a nonlinear PDE.


Hello All,

I looked through the Maple help on PDE systems and pdsolve and the physics problems that appear there. THere are a number of single-PDE cases with initial / boundary conditions; but I couldn't find PDE systems with ics/bcs.


Would you have a (simple) example of a PDE system with its initial / boundary conditions? I am attempting to build understanding of the syntax and different options of "pdsolve". Examples seem to be a great way to learn how to solve PDE systems. One can then pdsolve the PDE system without ics; then add them, try different options etc.


Thank you!


Hello All,

I have the PDE system shown below. It is a simple system for 2 unknown functions f1(x,t) and f2(x,t). Also, say we have x=x(t)=e^t for example. How does one solve such PDE system with Maple? I tried including the condition x=e^t in the PDE system itself, but got "System inconsistent" error message. x=x(t) can be looked at as an additional constraint and I am baffled how do I feed it into the PDE solver. 


Perhaps someone has experience with such systems?



Dear all,

I am trying to solve the following partial differential equation (transport or advection equation) with given initial and boundary conditions:

restart: with(PDEtools):
sys := [v*diff(u(x,t), x) + diff(u(x,t), t) = 0, u(x,0) = exp(-x), u(0,t) = sin(t)];

But it does not work. The solution is (or should be): 

u(x, t) = exp(t*v-x)+Heaviside(t-x/v)*(sin(t-x/v)-exp(t*v-x))

I think the reason is that the interval for t (in [0, inf)) and x (in [0, 1]) is not specified. On the other hand, this works:

restart: with(PDEtools):
sys := [diff(u(x, t), t) = diff(u(x, t), x, x), u(0, t) = 0, u(1, t) = 0, u(x,0) = f(x)];
sol := pdsolve(sys);

How can I solve a PDE like the transport equation with given initial AND boundary conditions?

Thanks a lot

I'm trying to build a Maple procedure that will generate vector fields on a metric with certain properties. Working with metric g over the coordinates {u,v,w}, call the field X = (a(u,v,w), b(u,v,w), c(u,v,w)). The field should satisfy <X, X> = 0 and have the directional covariant derivative of X in the direction of each coordinate vector field = 0 (with resepct to the Levi-Civita conenction).

Basically, these conditions yield a system of 3 PDEs and an algebraic expressionin terms of a,b,c. I've been trying to solve them using pdsolve, but I'm getting the error message:

>Error, (in pdsolve/sys) the input system cannot contain equations in the arbitrary parameters alone; found equation depending only on _F1(u,v,w): _F1(u,v,w)

I've attached my worksheet. Can anyone help me out?



I have the following PDE system to solve numerically and I am not sure how to use maple to solve it.


v_t = v_{xx} for 0<x<1 , t>0


v_x(1,t)=-hv^4(1,t) (where h is some numerical number);


To solve this pde numerically I need to use the following condition on v(1,t):

v(1,t) = 1-h*\int_{0}^t \theta_3(\tau)v(1,t-\tau)^4d\tau

this is the numerical boundary condition, where \theta_3 is Jacobi theta3 function.


I don't see how can I use maple for this numerical pde problem.


Here's my attempt at solution:


 PDE := diff(v(x, t), t) = diff(v(x, t), x, x);

JACOBIINTEGRAL := int(JacobiTheta3(0, exp(-Pi^2*s))*v(1, t-s)^4, s = 0 .. t);

IBC := {`&PartialD;`(v(0, t))/`&PartialD;`(x) = 0, `&PartialD;`(v(1, t))/`&PartialD;`(x) = -0.65e-4*v(1, t)^4, v(x, 0) = 1};

pds := pdsolve(PDE, IBC, numeric, time = t, range = 0 .. 1, spacestep = 0.1e-2, timestep = 0.1e-2, numericalbcs = {v(1, t) = 1-0.65e-4*JACOBIINTEGRAL}, method = ForwardTimeCenteredSpace)


But I get the next error message:

Error, (in pdsolve/numeric/process_IBCs) improper op or subscript selector


How to fix this or suggest me a better way to solve this pde numerically?



I need to solve the next ode:

diff(u(x, y), x) = -(2/3)*(3*h^3*nu+9*h^2*nu*y-12*nu*y^3+36*x^2*y+56*y^3)/h^3

diff(v(x, y), y) = (2/3)*(36*nu*x^2*y+56*nu*y^3+3*h^3+9*h^2*y-12*y^3)/h^3

diff(u(x, y), y)+diff(v(x, y), x) = -(6*(1+nu))*x*(h^2-4*y^2)/h^3

The inicial conditions are:

u(L, 0) = 0
v(L, 0) = 0
D[1]*u(L, 0) = 0

When I write on Maple this code, he give me a error:

with(PDEtools, casesplit, declare); declare((u, v)(x, y))

sys2 := [diff(u(x, y), x) = -(2/3)*(3*h^3*nu+9*h^2*nu*y-12*nu*y^3+36*x^2*y+56*y^3)/h^3, diff(v(x, y), y) = (2/3)*(36*nu*x^2*y+56*nu*y^3+3*h^3+9*h^2*y-12*y^3)/h^3, diff(u(x, y), y)+diff(v(x, y), x) = -(6*(1+nu))*x*(h^2-4*y^2)/h^3]

sol := pdsolve(sys2)

ics := u(L, 0) = 0, v(L, 0) = 0, D[1]*u(L, 0) = 0

pdsolve([sys2, ics]);

Why Maple can't solve this PDE?

I think that the problem is on sys2. But I don't know how to explain to Maple the function: diff(u(x, y), y)+diff(v(x, y), x) = -(6*(1+nu))*x*(h^2-4*y^2)/h^3; on the system of equations. I think the problem is there.

I'm so sorry by my bad english.

I need to solve this, anyone help me please.






I have a problem with maple solving diffusion equation. I solved the equation as follows

Es := 0.117108e12;
Ef := 0.78125e11;
l := 0.150e-6;
s := 0.500000e-3;
f := 0.5898334197e-6;
o := 0.9e-5;
d := 0.10e-17;
cb := 0.1e7/(19.9);
c := l*f/(d*cb);
PDE := diff(u(x, t), t)-(diff(u(x, t), x, x)) = 0;
IBC1 := {u(x, 0) = 0, (D[1](u))(0, t) = 0, (D[1](u))(1, t) = c};
S1 := pdsolve(PDE, IBC1, numeric, time = t);
S1:-plot(t = 0.6e-2);

i am plotting cincentration along the thickness of the material. i want to know why the concentration is negative. It should not be negative because constant flux 'c' is present at x=1. and flux at x=0 is 0, and also the initial concentration is 0.



Is it possible to somehow extract a derivative from numeric solution of partial differential equation?

I know there is a command that does it for dsolve but i couldn't find the same thing for pdsolve.

The actual problem i have is that i have to take a numeric solution, calculate a derivative from it and later use it somewhere else, but the solution that i have is just a set of numbers an array of some sort and i can't really do that because obviously i will get a zero each time.

Perhaps there is a way to interpolate this numeric solution somehow?

I found that someone asked a similar question earlier but i couldn't find an answer for it.


     I'm trying to numerically solve a PDE in Maple for different boundary conditions, however I'm having trouble even getting Maple to numerically solve it for simple boundary conditions.

I have cylindrical coordinates, r, z, theta, and I treat r = r(z, theta) for convenience to plot my solution surface. The initial coundary condition is that at z = epsilon (z = 0 is singular) , r = constant and of course r is periodic in theta. This is just a circle, and the analytical solution is know to be a half-sphere  r = sqrt(R^2 - z^2). I entered my initial boundary conditions into Maple, but it doesn't like the periodic one

IBC := { r(epsilon, theta) = R - epsilon__r,
              r(z, 0) = r(z, 2*Pi) };

  indepvars = [z, theta],
  time = z,
  range = 0..2*Pi);
Error, (in pdsolve/numeric/par_hyp) Incorrect number of boundary conditions, expected 2, got 1

I'm not sure how to make this work, and then generalize it to more arbitrary intial slices r(epsilon, theta) = f(theta).

Here's the attached worksheet,

Any help is appreciated,


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