# Questions tagged [boundary-conditions]

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### R-K fourth order scheme for system of ODEs containing 32 differential equations

In the present code, I am trying to solve the system of differential equations using the R-K fourth-order scheme. I am trying to plot the function u and T, but it is showing some error in the boundary ...
126 views

### Spherical Heat Equation and Convection Boundary Conditions

I'm trying to solve transient heat conduction equation in spherical domain in Mathematica. I made the simplifying hypothesis that temperature varies only with time and radial coordinate. The code is: <...
29 views

### NDSolve diverges with Neumann boundary condition [duplicate]

I am solving Poisson-like PDE with the Finite Element Method in Wolfram Mathematica. Only the Neumann boundary condition is imposed on the boundary. Of course, the solution is not unique, most likely ...
42 views

### Graph plotting using system of ODE with NDSolve command

In the present question, I am trying to solve a system of ODEs with corresponding boundary conditions. And then, trying to plot the velocity function, but it shows some errors. Can anyone please help ...
198 views

### Solving a one-dimensional free-boundary problem with a singular boundary condition

Addendum (orginial question below). Thank you for the responses! After thinking some more about this problem, and thanks to @bbgodfreys helpful comment, I realised that the problem as posted below is ...
233 views

### How to accelerate FindRoot?

Original: I am running the following code to find the root of F , T and MM, here is an example ...
1 vote
79 views

### On formulating a Neumann boundary condition

I am attempting to follow this tutorial in the documentation on using FEM to solve PDEs. I am having difficulty understanding how to formulate the Neumann boundary condition for my free-boundary ...
1 vote
86 views

71 views

### Non-minimal coupling ξ , Minkowski false vacuum decay case (shooting method) (An update to the previous question)

I asked a few days ago this question: Non-minimal coupling ξ - numerical bounce solutions (shooting method, false vacuum decay) Alex Trounev helped me improve my code building based on this paper (...
137 views

### NDSolve with parametric endpoint

I want to solve numerically a system of ODEs of the form: $$\ddot{y}+3\frac{\dot{b}}{b}\dot{y}=2Cy(y^2-1)$$ and $$\dot{b}^{2}=1-b^{2}+\frac{D}{2\sqrt{C}}b^{2}\left(\dot{y}^{2}-C(y^{2}-1)^{2}\right)$$ ...
47 views

### Constraints in a set of equations

I am currently working on a system of equations that is subject to a determinant constraint. Specifically, I have a matrix $B$ with $\det(B) = 0$, and I aim to construct a linear combination of its ...
1 vote
125 views

### Non-minimal coupling ξ - numerical bounce solutions (shooting method, false vacuum decay)

I have the potential below: $$V(\phi)=-\frac14 a^2(3b-1)\phi^2+\frac12 a(b-1)\phi^3+\frac14 \phi^4 +a^4c$$ This potential has 2 minima, the false vacuum $\phi_f=0$ which tunnels to the global minimum, ...
148 views

### DSolve solution for 1st order PDE involving complex number does not match initial condition

Bug introduced in 11.3 or earlier, persisting through 13.2.1. [Mathematica 12.0.0.0, MacOS X x86 (64bit)] Trying to solve ...
73 views

### How to solve boundary value problem?

Is it possible to solve a boundary value problem like this? ...
129 views

### How to specify derivative boundary conditions for the gradient to be normal to the boundary?

I'm currently modeling an electric field with 2 charges. To do so, I use NDSolveValue to solve a Laplacian with 2 Dirichlet conditions on the voltages of the ...
131 views

### Shooting technique using NDSolve

Here I am attaching my code below. It took all the variable's values, but the graph window was empty. I am not able to recognize, where is the error exactly. Differential equations were also, checked ...
1 vote
95 views

### Shooting technique [closed]

Here is my code, I am trying to plot the graph of the differential equation, But output graph is an empty window. can anyone please help in getting the graphs. This equation is a modified bessel ...
18 views

### Difference Equation with Upper Boundary Condition, Lower Terms Not correct

I am struggling to understand the solution Mathematica is providing for the following recurrence relation As I have written a[i] I expected the following behavior <...
87 views

### Findroot: Boundary value problem

I have an equation, ...
99 views

### Implementation of Neumann-like boundary condition

If we wish to solve an elliptic PDE, say $\nabla^2\phi=\text{given}$, on a domain $\Omega$ with Neumann boundary conditions, $\hat{\mathbf{n}}\cdot \nabla \phi\Big|_{\partial \Omega}=\text{given}$, ...
1 vote
91 views

### Plotting the solution of an equation

I just wondering if I can plot this solution? FullSimplify[Integrate[1/Sqrt[-1 + f/3 x^2 + b/x], x] , Assumptions -> {x > 0, f > 0, b > 0}]
94 views

### A Simple Integrate

I'm facing the integral ...
90 views

### Solve an equation for different values

I was trying to solve this equation for different value of a constant (a) but the solution is not different for those values?!! b and m are positive values. ...
160 views

### Unstable boundary values using NDSolve?

I have an equation: w1[u_]=-(1/2) u^2 ea e0 Sin[2 a[z]] + K (a''[z]) with numerical values, ...
362 views

### How can we apply specific boundary conditions with NDEigensystem?

I'm solving an eigenvalue problem with special b.c. mentioned in the paper Edge states in gated bilayer-monolayer graphene ribbons and bilayer domain walls. (See Eq.(3)(6)(7) and the paragraph after (...
372 views

### False vacuum bounce solution (curved space) shooting method problems

Merry Christmas, I think I can still say it. I am back this time for my problem in a simpler case, without coupling. I have a problematic code now and I want your help. I want to solve numerically the ...
152 views

### NDSolve Extrapolating boundary conditions for FiniteElements

I'm trying to solve a 1+1 (1d time + 1d space) partial differential diffusion equation. My NDSolve call look basically like this: ...
217 views

### Coiling of flexible ropes (nonlinear BVP of ODEs with 10 unknown functions and 2 parameters)

I want to solve this ODEs with NDSolve, but it fails. The $F$(F), $\gamma$ (γ) is the given ...
1 vote
177 views

### Solving Laplace PDE in mathematica

I'm trying to get the general solution for the Laplace equation: $\frac{\partial^2 V}{\partial x^2} + \frac{\partial^2 V}{\partial y^2} = 0$ on the domain \$\mathbb{R_0}\times\mathbb{R^+}\backslash\{(0,...
327 views

### Numerical solution of a partial derivative problem

WARNING: a couple of days ago I posted a similar question, but due to the impossibility of DirichletCondition[] to handle "cross-coupling of dependent ...
278 views

### I want to plot the solution but

I want to plot this solution for the different value of d and x but it is an Elliptic function. ...
205 views

### First order Differential equation with boundary condition

I'm wondering why it is not solving with the Mathematica?? ...
I'm working on getting a numerical solution for the following PDE: $$u_t-u_{xx}=0,\ x\in[0,1], t\in[0,1],\\ u(x,0)=\sin(2\pi x),\\ u(0,t)=0,\\ u_x(1,t)=2\pi e^{-t}.$$ The hand solution for this PDE ...