Questions tagged [boundary-conditions]

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NDSolve Convergence Issue for Coupled Field Problems

I have tried to use NDSolve to solve a coupled field Eqs (see the attached Codes). The MMA solver seems to failed to converge to the requested accuracy or precision within 100 iterations ...
89 views

Periodic extrapolation out of the domain of the solution of a PDE in two directions

As a prototypic problem ...
2k views

Three dimensional Laplacian insulated on lateral faces and convectively exposed on transverse faces (updated)

I have the three dimensional Laplacian $\nabla^2 T(x,y,z)=0$ representing temperature distribution in a cuboid shaped wall which is exposed to two fluids flowing perpendicular to each other on either ...
219 views

How to solve Nonlinear coupled ODEs using DSolve

I cannot solve such a system of coupled ODEs in MMA 12.1 using DSolve. i.e. output is equal to the input equations ... (see the attached figure) Here, each solution is labeled according to the name of ...
40 views

How to specify the initial conditions with ParametricNDSolve

I am still working on this problem. I am trying to use shooting method since I do not know the correct value for the initial derivative. I am following this answer. Now the code looks like this (I ...
303 views

Two-dimensional Laplacian coupled with another equation leading to a BVP with integral bc(s)

I have the two-dimensional Laplacian $(\nabla^2 T(x,y)=0)$ coupled with another equation. The Laplacian is defined over $x\in[0,L], y\in[0,l]$. On manipulating the second equation (which I have ...
320 views

Solving pde with boundary integral constraint

I want to solve a PDE, but I'm struggling a lot getting it into Mathematica. This is what I currently have (thanks to @user21). However, there are still a couple of issues which I explain below. ...
190 views

Specify a force on the entire body (e.g. gravity)

In the thread Stress calculations using finite elements User21 showed an example how to define a force over the entire body during FEM calculation as boundary condition. See the screenshot below from ...
277 views

Balanced flux in FEA using NeumanValue

I'm using NeumannValue boundary conditions for a 3d FEA using NDSolveValue. In one area I have positive flux and in another area i have negative flux. In theory these should balance out (I set the ...
46 views

How to define more general boundary conditions for ConvolutionLayer?

In Mathematica 12, I only see the option to define "PaddingSize" for a ConvolutionLayer in order to get Dirichlet boundary ...
366 views

Mathematica vs. MATLAB: why am I getting different results for PDE with non-constant boundary condition?

I am trying to solve the same PDE in Mathematica and MATLAB, $\nabla^2\phi=0$ where $\phi=f(x,y)$ It has a Dirichlet boundary condition on the left, a section of non-constant Neumann boundary ...
239 views

PDE solving for two different regions?

I have searched and read all previous questions but cannot get my head around this. I am new to mathematica. I have two regions in 2D where I want to solve PDE. Of the form: ...
58 views

Full domain of Dirichlet boundary not displaying in 3DPlot

I have code to solve the 2D wave equation on a given region with an initial condition that is sinusoidal in one part of the region and 0 elsewhere. Here is an example on a rectangular region that ...
78 views

Modelling transparent boundary conditions on a quantum graph with Mathematica NDSolve and finite-element method [duplicate]

Continue to this issue I am now trying to apply a solution from the question above to three-bonded star graph. My idea is to take the third bond at [10,20] because I am using only one function u[t,x]....
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Error in the solution of PDE with NDsolve and method of lines [closed]

I am trying to solve a system of the partial differential equation with the help of NDSolve and method of lines. Mathematica code for the above-described problem is ...
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"Fewer dependent variables than equations, so the system is overdetermined" without any BC's

Consider this system of PDEs. eqn1 = D[u[x, t], x] + 5 D[u[x, t], x, x] + D[v[t], t, t] - 4 == 0 eqn2 = D[v[t], t] + D[u[x, t], t, t] + v[t] == 0 I would like to ...
158 views

Solving Piecewise Differential Equation using NDSolve (coupling at BC)

I am having some issues in dealing with a system of differential equations. I would like to solve a 1D diffusive heat equation across several regions with different material properties. I now have a ...
68 views

BVP rooting method [duplicate]

How can I get the value of u'[-1], how can I know the StartingInitialConditions it used, why the output is just one solution ...
151 views

How to solve an under determined system for a ratio of variables?

I have two equations in 3 variables a2, b1, b2: ...
179 views

Consider the following ODE for $y(x)$ over $x\in\left[0,\frac{1}{2}\right]$ with an eigenvalue $\lambda$ $\qquad 2x\,y''''+ 4y'''=\lambda\, y''$ The boundary conditions at $x=\frac{1}{2}$ are $y'\... 2answers 150 views How to connect boundary points of graph I have the following data; ... 1answer 223 views Simplifying solution to a third-order Boundary Value problem I have been trying to solve a physical problem during which I reach the following third-order, Linear O.D.E. The solution I get using this expression is really messy. Is there any way to simplify it ... 0answers 63 views Improving NDSolve robustness (not blowing up) I am trying to solve a heat conduction equation in Mathematica 9. While I can get NDSolve to work in some conditions it appears to arbitrarily fail if parameters are modified even slightly. Eventually ... 0answers 201 views Solving time dependent boundary conditions heat PDE I am attempting to solve the heat equation$\frac{\partial T}{\partial t}=\nabla^2T$, where$T=T(x,y,z,t)$, subject to the following boundary conditions:$\frac{\partial T}{\partial x}|_{x=10}=\frac{\...
I tried to solve a fourth-order eigenvalue problem with boundary conditions on high order derivative. For example, the following equation, \frac{\partial d}{\partial t}+\frac{\partial^4 d}{\...