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Questions tagged [boundary-conditions]

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70 views

How to solve transient 3D heat equation with robin boundary conditions

Good afternoon! I'm trying to solve the following heat equation: with the following boundary conditions and initial value: Nut I'm getting error while solving it with NDSolve: ...
61 views

Numerically solving a system of ODEs with parameters [on hold]

I am working on solving a system of coupled ordinary differential equations with initial values given. When I searched about my requirements I got the similar answer here. But I got another condition ...
50 views

How do I formulate a Dirichlet boundary condition for which the boundary depends on the other variable?

I am trying to solve the Poisson equation on a cylindrical grid. $$\frac{1}{r^2} \frac{\partial}{\partial r} r^2 \frac{\partial f(r, \theta)}{\partial r} = n(r, \theta)$$ Analytically, there is ...
67 views

Problems with Neumann (zero flux) boundary conditions

I have the following code: ...
202 views

Thermal conduction (Annulus, 2D): Missing boundary conditions

The thermal conduction problem, described in polarcoordinates can be solved ...
67 views

Unable to use ElementMarker in DirichletCondition with structured quad mesh

I would like to use ElementMarker in a DirichletCondition on a structured quad mesh, but I am receiving the error: ...
67 views

1D transport equation with Neumann conditions

I'm trying to solve 2nd order differetntial equation of heat transfer-type in a finite system x<0,L>, in particular: ...
139 views

Wave equation: Understanding PeriodicBoundaryCondition

Inspired by the interesting question 202542 I try to solve the wave equation with coupled boundary conditions u[x,t==1 ]==u[x,t==x/2] I tried ...
37 views

Setting custom boundary conditions in pdetoode [closed]

I am solving a mix of PDE and ODE for two functions c1(x,t) and c2(t). Several answer point to the use of the function pdetoode. I would like to use that function, but set the my own boundary ...
191 views

How to solve PDE with periodic and anti-periodic b.c.?

I need to solve the PDE for a complex function $A(x,t)=A_r(x,t)+iA_i(x,t)$ ...
73 views

How to impose a “boundary” condition inside a computing domain?

I need to set a "boundary" condition not at the boundaries of the computing domain but inside the domain during solving an ODE with FDM. The problem is a boundary value problem, which has been ...
73 views

Errors from NDSolve [closed]

I'm trying to solve a system of PDEs with periodic boundary conditions using NDSolve. This works if I don't specify an initial condition (but is uninteresting, ...
29 views

How to put boundary condition for linear set of differential equation?

I have the following code. ...
65 views

Variation of the biharmonic equation with Neumann conditions

I am currently writing a script to plot the solution of a variant of the biharmonic equation. In this case the equation I want to solve is ...
58 views

297 views

NDSolve error in 2-D heat equation

I'm trying to solve the following PDE by Mathematica in 2-D case in the unit disk using polar cordinates, where $\Omega$ is a bounded domain of $\mathbb{R}^n$, $\Gamma =\partial \Omega$ is the ...
68 views

622 views

Inhomogeneous Neumann boundary conditions for diffusion equation

I am new to Mathematica and I have a problem specifying Neumann boundary conditions in diffusion equation. The best result I managed to get is this. ...
34 views

NDSolve: Method of Lines: same grids for spatial discretization: error: stiff system_zero step size

How can I modify bbgofrey's answer so as to use $n+1$ grid points for variable $y$? My code ...
85 views

EDP exotic boundaries condtions

I'm trying to numerically solve Laplacian(V(x,y)) = 0 on a cross having Dirichelet conditions on two opposite borders (e.g. V(0,x)=-10 and V(5,y)=-10) and having dV(x,y)/dx = const . dV/dy for ...
134 views

NDSolve:Method of Lines: Spatial Discretization: bother doing it explicitly or just implement as internal routine?

My question is whether one's code must always contain the actual description of spatial discretization written explicitly or whether the Method of Lines can be called as an internal routine. If so ...
164 views

I tried to NDSolve the PDE system $$\partial_t w =x\cdot w\quad\quad\partial_z x=w$$ for $$(t,z)\in[0,1]\times[0,\pi]$$ with boundary conditions $$x(t,0)=w(t,0)=w(t,\pi)=0$$ and initial conditions $$w(... 2answers 206 views NDSolve:Coupled PDE's, initial-boundary value problem: unreasonable “insufficient number of boundary conditions” error I tried to NDSolve the PDE system:$$\partial_t y = x\partial_z w \quad\quad \partial_t w = \partial_z y \quad \quad \partial_z x=w $$for$$(t,z)\in[0,1]\times[-1,0]$$with initial conditions$$x(...
NDSolve can easily handle the PDE system $$\partial_t y = \partial_z w \quad\quad \partial_t w = \partial_z y$$ along with initial-boundary conditions w(t,0)=w(t,-1)=0\quad\quad w(0,z)=-sin^2(z\pi)\...