# Questions tagged [boundary-conditions]

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### Problems with boundary conditions

I am new to mathematica and I have doubts with my code, I probably have errors with the boundary conditions If you could help me I would appreciate it very much my code is the following ...
45 views

### Give NeumannValue a nonlinear function

I have the following simpler example of my actual problem which reproduces my question ...
132 views

### Finding solution for larger intervals with shooting method

I am trying to solve numerically the following non linear differential equation: $y''(x)+\frac{3}{x}y'(x)=\frac{{\rm d}V(y)}{{\rm d}y},\qquad V(y)=\frac{1}{4}(y(x)^2-1)^2+\frac{a}{2}(y(x)-1),$ with ...
64 views

### Analytical solution for ODE with a power-law term?

I want to solve the following differential equation which is a very common growth law model in biology — a generalization of the logistic equation. In this case, the equation possesses a power-law ...
73 views

### Boundary condition dependence on NDSolve inconsistent

In attempting to solve a fourth order system I have encountered an issue with the way NDSolve uses boundary conditions. Consider the following three different attempts: ...
91 views

### General:: Exp[-717.401] is too small to represent as a normalized machine number; precision may be lost

I am solving pde. For the post processing below, there is solution given in output which is the solution from mathematica version 10.0.1. ...
107 views

### Solve coupled partial differential equations with absorbing BCs

I try to solve the following system of coupled equations with NDSolve but the results seem to be not correct. I attached my code in which five dependent variables $f_{1}$, $f_{2}$, $f_{3}$, $f_{4}$, ...
138 views

### Solving a Modified Biharmonic Equation on a Square

I am seeking to solve the differential equation \begin{equation} \left[\partial_{\overline{x}}^{4}+2\left(1+\delta\right)\partial_{\overline{x}}^{2}\partial_{\overline{y}}^{2}+\partial_{\overline{y}}^{...
566 views

### Solving heat equation on a cylinder with insulated ends and convective boundary conditions

I am trying to solve heat equation on a cylinder whose ends are thermally insulated and its circular face is exposed to convection. Therefore I have Neumann boundary condition on all faces of the ...
89 views

### PDE with boundary condition (differential equation)

I am trying to find a solution to this boundary value problem $$h_t= \frac{1}{2} \sigma^2 x^2 h_{xx} + r x h_x \quad s.t.\\ Ah(b,t)+Bh_x(b,t)=g(t),$$ where $A,B,\sigma,r,b$ are constants and $g(t)$ ...
207 views

### Geometrically nonlinear beam deflection

Edit only for those interested in large deflections of beams I discovered a mistake in the equations of the original question (below): in the normal force (compression/traction) ...
82 views

### Error when using NDSolveValue. Lists are not the same shape

Please, help me with the following issue. I am solving the following system of the coupled PDEs with the following boundary conditions and initial conditions. After performing the following ...
57 views

### NDsolve Boundary Condition is a Function of the Solution

I am trying to solve something like Fick's Law using NDSolve: $$\frac{\partial \varphi}{\partial t}=\frac{\partial^2 \varphi}{\partial r^2}+F(r,t)$$ Subject to a ...
79 views

### Shooting Method with extra Unknown Condition

I've been trying to solve a system of 3 coupled 2nd order ODEs, for a real variable $x$, $0\geq x\leq \infty$. The equations are the following: \begin{align} &x^{2}\,h''(x) - x\,h'(x) + x^{2}\,g^{...
68 views

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### Numerically Solving a system of PDE (2 unknown functions)

I need to solve for function H[x,y] and V[x,y] on square {x,0,1},{y,0,1}, obeying the ...
74 views

### Having error with solving BVP problem

I am trying to solve this differential equation but using my approach: ...
95 views

### Assigning ElementMarkers to existing ElementMesh boundaries

I've imported a 2D element mesh from another program as a list of triangle coordinates {{x1,y1},{x2,y2}....} ("nodes") and element connections {{n1,n2,n3},...} ("elements"). Then I create an ...
199 views

### DEigensystem gives x-dependent eigenvalues

Bug introduced in Version 11 or earlier and persisting through 12.1. Reported to Wolfram Technical Support as CASE:4532301. I am considering the eigenvalue problem associated with the double-well ...
116 views

### Trouble with dependent variables in NDSolve while modelling transparent boundary conditions on a quantum graph with Mathematica

I am trying to create a model of plane wave's propagation on a quantum graph(metric graph with a differential operator, Shrodinger operator in my case, along the edges and continuity condition at the ...
254 views

### How to define the boundary condition in 1D Heat transfer

I am trying to calculate the heat transfer among a 1-D rod, with one end insulated while the right end is immersed in constant temperature surface T=0. Assume that the initial temperature of the rod ...