Items tagged with pde pde Tagged Items Feed

Is it possible to solve piecewise differential equations directly instead of separating the pieces and solving them separately.

like for example if i have a two dimensional function f(t,x) whose dynamics is as follows:

dynamics:= piecewise((t,x) in D1, pde1, pde2); where D1 is some region in (t,x)-plane

now is it possible to solve this system with one pde call numerically?

pde(dynamics, boundary conditions, numeric); doesnot work

pde system solve ...

June 24 2014 wo0olf 15


i obtained values for h(t) and u(t) and i wana obtaine s(t) , i don't konw how can i do it


for h(t) and u(t) ,


sol1 := dsolve([4.00000000000000*u(t)^2*h(t)*(diff(diff(h(t), t), t))-8.00000000000000*h(t)^2*(427.2460938*u(t)+385620.1174/u(t)-25671.38673)^2+16.0000000000000*u(t)*h(t)*(427.2460938*u(t)+385620.1174/u(t)-25671.38673)*(diff(h(t), t))+(16406.2500000000*(-29.8200000000000+u(t)))*h(t)^2*(427.2460938*u(t)+385620.1174/u(t)-25671.38673)+7171.87500000000*u(t)*h(t)*(diff(h(t), t))-16406.2500000000*h(t)^2*(30-u(t))*(427.2460938*u(t)+385620.1174/u(t)-25671.38673)+u(t)^2*h(t)-0.225000000000000e-1+0.225000000000000e-1*(.997494986604054+.106105802501554*sin(t-1.5))^2+4.00000000000000*(h(t)*(427.2460938*u(t)+385620.1174/u(t)-25671.38673)+u(t)*(diff(h(t), t)))^2 = 0, diff(u(t), t) = 427.2460938*u(t)+385620.1174/u(t)-25671.38673, h(1.44) = 0.145e-4, (D(h))(1.44) = .12093, u(1.44) = .62], numeric)


and s(t) is , s(t)=1/r*d/dt(u(t)*h(t))



How do I find the constants in a solution containing whittaker functions?

the boundary conditions are:








When trying to find the fundamental solution of the Heat equation using Maple (software), I get the following Error message which seems to have no documentation available (?) :

Using :

          PDE := -(diff(f(x, t), t))+(diff(f(x, t), x, x))*Di = 0

assume(epsilon > 0);

pdsys := [PDE, f(x, 0) = Dirac(x-epsilon)];

pdsolve(pdsys, build)

"Error, (in casesplit/K) this version of casesplit is not yet handling the function: Dirac"

Anybody has an idea what that is? (Using Maple 17) . How can I solve this problem ?


Thanking you on Advance, 

Erez . 


I try to solve this equation using pdsolve but there is no results.

Eq:=diff(u(t,x), t$2) =diff(u(t,x),x$2)+sin(u(t,x));


Thank you for your help.


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. 

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.

i am solving 4 ODE with boundary condition..

> restart;
> with*plots;


then i got this error..

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system


i dont know where i need to change.. could you help me..




How can I use separation of variable to solve heat equation ut=uxx on a rod of length pi/4 with u(0,t)=0, u(pi/4)=0 and u(x,0)=x(pi/4-x) 

then solve heat equation by laplace transform

Dear all,

I need your help.

I compute the exact solution u(x,y,t) os PDE.
My code :

I would like to plot the exact solution of my PDE.

My method work well but  when I put a:=1; b:=1; In the next lines there is no change, always I have a and b in my equation.

If i fix the time, "t=1 or 2 " for example; In the last lines i plot( u(x,y,2)); but doesn't work also.

Then animation in "t" how....

Thanks for your help.




Does anyone has any maple worksheet that generate surface using the PDE method described in this article?  I am trying to learn this method but I am not familiar with the mathematics to do it although the paper gives some description of it.  I hope someone can demonstrate the procedure in Maple.  Thanks

Dear All, I need your help to plot the numerical solution. many thanks.

The variable t in [0,T], x in [0,1], b in [0,2].

Difference finie for waves equation is :

pde:=diff(u(x, y,t), t$2) = c^2*(diff(u(x, y,t),x$2)+diff(u(x,y,t),y$2));

i: according to x, j according to y, and k according to t.

u[i,j,k+1]=2*u[i,j,k]-u[i,j,k-1]+(c*dt/dx)^2*(u[i-1,j,k]-2*u[i,j,k]+u[i+1,j,k])+ (c*dt/dy)^2*(u[i,j-1,k]-2*u[i,j,k]+u[i,j+1,k])


Boundary condition: u(t=0)=1, diff(u(x,y,t),t=0)=0, and the normal derivative on the boundary of Omega =0.

How can solve this problem and plot the numerical solution.




Pls, I tried solving the system of PDE numerically.... When I did for just 1 plot, the graph was plotted but When I varied some parameters its not coming out.... Also, its not bringing any error so I can't trace out my PLS HELP ME OUT with the multiple plots... Attached are my source codes links....


dchange pde maple...

March 13 2014 sarra 170

Dear all,

I need your help

I have a problem with dchange ....  use the dchange command to transform pde to the
                                 x[1], x[2].


> restart;
> with(PDEtools); with(LinearAlgebra);
> pde := diff(u(t), t, t)+2*GAMMA*(diff(u(t), t))+omega^2*u(t) = 0;
           / d  / d      \\           / d      \        2         
           |--- |--- u(t)|| + 2 GAMMA |--- u(t)| + omega  u(t) = 0
           \ dt \ dt     //           \ dt     /                  
> deq1 := diff(u(t), t) = v(t);
                               --- u(t) = v(t)
> deq2 := subs(deq1, pde);
                 / d      \                       2         
                 |--- v(t)| + 2 GAMMA v(t) + omega  u(t) = 0
                 \ dt     /                                 
> dsolve({deq1, deq2}, {u(t), v(t)});
> eqns := [rhs(deq1) = lhs(deq1), rhs(deq2) = lhs(deq2)];
       [        d            / d      \                       2     ]
       [v(t) = --- u(t), 0 = |--- v(t)| + 2 GAMMA v(t) + omega  u(t)]
       [        dt           \ dt     /                             ]
> y := [u, v]; b := diff(y(t), t);
                                   [u, v]
                            [ d         d      ]
                            [--- u(t), --- v(t)]
                            [ dt        dt     ]
> A, b := GenerateMatrix(eqns, y(t));
          Matrix(%id = 122038892), Vector[column](%id = 135944696)
 # Return a vector of eigenvalue of A and matrix  whose columns are eigenvectors of A
> gnat := Eigenvectors(A);
> lambda := gnat[1]; Lambda := gnat[2];
                       Vector[column](%id = 135975976)
                           Matrix(%id = 136787860)
> Y := Vector([y]);
                       Vector[column](%id = 123771808)
> tr := solve(GenerateEquations(Lambda, [x[1], x[2]], Y), {u, v});
     /           /                                    (1/2)             
     |      1    |                   /     2        2\                  
    < u = ------ \-x[1] GAMMA - x[1] \GAMMA  - omega /      - x[2] GAMMA
     |         2                                                        
     \    omega                                                         

                               (1/2)\                 \
              /     2        2\     |                 |
       + x[2] \GAMMA  - omega /     /, v = x[1] + x[2] >
> dchange(tr, pde, [x[1], x[2]]);

hi,i want to take differential with respect to another differential using physics package,but using D instead of diff,could anyone help me do that ? for example :

restart; with(Physics):
A1 := -(1/24)*1*rho*((diff(phi[1](x, t), t))^2)*(h^3)-(1/2)*1*rho*((diff(u[ref](x, t), t))^2)*h-(1/2)*rho*((diff(w(x, t), t))^2)*h+(1/24)*1*1*((diff(phi[1](x, t), x))^2)*(h^3)+(1/2)*1*(1*((diff(u[ref](x, t), x)+(1/2)*(diff(w(x, t), x))^2)^2)+K*1*((diff(w(x, t), x)+phi[1](x, t))^2))*h-1*q*w(x, t):


here i want to compute A2 using D command,not diff and i do not want use convert command ! i just need to calculate A2 directly using D command. tnx for your help.


1 2 3 4 5 6 7 Page 1 of 7