Linked Questions

21 votes
1 answer
2k views

Couple a PDE and ODE in NDSolve

I would like to solve an example of non-stationary heat transfer with a coupled PDE and ODE. Let's assume that we have 1 dimensional bar of length $L$ with uniform initial temperature. The right end ...
Pinti's user avatar
  • 6,513
2 votes
1 answer
2k views

Solving coupled PDE and ODE

I want to solve a system of partial differential equation in Mathematica. equation is: $ y_0 = 0.5, t_0 = 30, λ_{12} = 0.3, λ_{13} = λ_{23} = 0.01, λ_{21} = 2.8 $ I am new in Mathematica. Please help ...
sara's user avatar
  • 21
6 votes
1 answer
573 views

Simulating a combination of PDEs and ODEs

I am trying to simulate a combination of PDEs and ODEs, given below. $$ \begin{matrix} -L\dfrac{\partial}{\partial t}I(t,z)&=&\dfrac{\partial}{\partial z}V(t,z)+RI(t,z)\\ C\dfrac{\...
kosa's user avatar
  • 495
3 votes
1 answer
1k views

NDSolve: Couple PDE and ODE involving integral

I am trying to numerically solve an equation with NDSolve, where there is a ODE coupled to a PDE, like the following: ...
Lufu's user avatar
  • 51
5 votes
1 answer
508 views

1-D PDE with nonlinear ODE as boundary condition

Recently, I am trying to solve a 1-D PDE with a nonlinear boundary condition using the function NDSolveValue. However, it seems that MMA (12) cannot solve it directly with some computational issues. ...
LingLong's user avatar
  • 329
3 votes
1 answer
2k views

NDSolve two PDE plus one ODE, together

I have a couple of PDE (time and space/length) that are correctly managed by NDSolve, but to which I’m adding an ODE on which the acc “accumulates”, through time, a ...
P. Fonseca's user avatar
  • 6,675
0 votes
0 answers
611 views

NDSolve a system of one PDE coupled with an ODE

I would like to solve a partial differential equation where one of the boundary conditions is the solution of an ordinary differential equation that is coupled to the partial differential equation. ...
Rischaard's user avatar
1 vote
1 answer
197 views

Numerically solve of a system of PDEs

I am studying the vibrations of a beam which is coupled to piezoelectric strips. This system is described by the following system of DEs: ...
Eduardo's user avatar
  • 13
2 votes
1 answer
247 views

Coupled PDE system in atomic physics

My question is about the implementation of a system of coupled PDEs to Mathematicas NDSolve routine. I'm considering one-dimensional toy model in atomic physics. The model describes two fields $\psi =\...
Hamilcar's user avatar
  • 133
1 vote
0 answers
244 views

PDE: Specify AccuracyGoal, StepSize, and WorkingPrecision interval-wise [closed]

I am using Mathematica 8. I have two ODEs (in time) and a diffusion PDE (in radius and time) which are all coupled to each other. I solve them using NDSolve by ...
Sanya's user avatar
  • 143
0 votes
0 answers
55 views

Solving matrix system of ODE coupled to a non linear PDE (Reynolds)

I am trying to solve the following problem for $p$ (the pressure) between a piston skirt and a cylinder lining. This depends on the secondary motion of top and bottom of the piston skirt $e_t$ and $...
Martin's user avatar
  • 1