Questions tagged [boundary-conditions]
The boundary-conditions tag has no usage guidance.
177
questions
0
votes
0answers
46 views
Conjugated Diffusion Equations
I am new to mathematical-biology and I have to solve the following (diffusion-like) equation
\begin{eqnarray}
\frac{\partial a(x,t)}{\partial t}= D \frac{\partial^2 a(x,t)}{\partial x^2}\\
\frac{\...
7
votes
2answers
399 views
Solving a 2D heat equation on a square with Dirichlet boundary conditions
I am trying to solve the following heat equation problem on the square [0,1]x[0,1].
\begin{equation*} \begin{gathered} u_t = u_{xx} + u_{yy} + f(x,y,t), \qquad u(x,y,0) = 0, \qquad u=0 \text{ on ...
4
votes
2answers
141 views
Is Shooting the best NDSolve method for two point conditions, and how to improve its accuracy?
Hi I have a two point conditions problem (controlled SIR epidemics via Pontryagin BVP), which is supposed to depend heavily on initial conditions, which break the problem into several cases (...
5
votes
2answers
170 views
Solving a heat equation on a finite interval with Neuman boundary conditions
I am new to Mathematica and need to verify my numerical result.
Can anyone please show me how to solve the following heat equation problem $$ u_t = u_{xx}$$
on the interval $ x \in [0,1]$. The initial ...
2
votes
1answer
59 views
NDSolve to automate shooting method (or others) for free boundary value problem?
I am trying to solve the following system of differential equations using NDSolve:
$$
\begin{align*}
f'(s) &= \frac{f(s)}{g(s)-s}\\
g'(s) &= \frac{g(s)}{f(s)-s}\\
f(0) &= 0\\
g(0) &= 0\...
4
votes
1answer
80 views
Solve numerically 2D parametric boundary problem
For a personal project, I want to solve the following problem:
Let $f\left(\boldsymbol{r}\right)$ be a 2D function, and let $\boldsymbol{r}\left(s\right)=\left(x\left(s\right),y\left(s\right)\right)$ ...
0
votes
0answers
52 views
Solving partial differential equation
I am new to mathematica and I want to solve the following pde. I have two boundary conditions and one initial condition.
I have tried the following code but the output is not the solution and it's ...
0
votes
1answer
82 views
Trying to find values of two parameters that match the boundary conditions defined
I have been trying to solve for the values of two parameters that satisfy the boundary conditions set for a set of equations set. The below is the code.
...
1
vote
1answer
51 views
DSolve a partial differential equation with two boundary conditions
While trying to solve:
$$
z \frac{\partial}{\partial z} (z G(s,z))=z \cosh (s) \frac{\partial}{\partial z} G(s,z)-\frac{1}{2}
\sinh (s) \frac{\partial}{\partial s} G(s,z)
$$
using DSolve it gives a ...
0
votes
0answers
58 views
Second-order nonlinear ordinary differential equation with some conditions
I just started to solve second-order nonlinear ordinary differential equation with boundaries condition I wanted to solve by DSolve but I know should be some ...
1
vote
0answers
60 views
DSolve for deflection of an elastic beam
I have to write a notebook about comparing the results of the deflection of an elastic beam, calculated with discrete methods and FE methods. The code has to be generalized for any kind of beam ...
4
votes
2answers
126 views
Numerically solve PDEs with constraints and without boundary solution
I have a PDE like
D[h[x1, x2], x1]*a[x1,x2]+D[h[x1,x2], x2]*b[x1,x2] + c[x1,x2] == h[x1,x2]
s.t. gradient(h(0,0))==0
where a,b,c are known functions of x1 and x2, ...
0
votes
1answer
50 views
How do I add a velocity boundary condition with specific time period
I have a wave equation for displacement and velocity, I want to add this boundary condition $v(x=0,\,t>0)=1$
My mathematica code is
...
1
vote
1answer
136 views
How can I solve a system of PDEs with constraints but having unknown boundary conditions
I have a 1st order system of two PDEs with two independent variables and two dependent variables.
...
2
votes
0answers
91 views
Trying to solve a PDE ā getting warnings I don't understand
Consider the partial differential equation
...
0
votes
0answers
69 views
How to impose null divergence in the solution of NDEigensystem
I am trying to use NDEigensystem to find eigenvalues and eigenmodes of the following Laplacian with boundary conditions:
$$\vec{\nabla}^2 \vec{A}(x,z) = vals \; \...
2
votes
1answer
66 views
Trying to solve non-linear coupled differential equation with boundary conditions at different points
I'm trying to solve systems of dif. equations with boundaries conditions at distinct points such as:
...
1
vote
0answers
31 views
How to define smooth random initial conditions consistent with boundary conditions for this 1+2D PDE?
I wrote a fully working code to numerically solve a non-linear variation of the classic 1+2D waves equation. Here's a stripped down version of it (classic waves equation), with static initial ...
1
vote
1answer
83 views
Solving a system of PDE-ODE with Dirichlet condition
I'm trying to solve a system of one PDE and one ODE that are dependent on time and distance (H[x,t] and P[x,t]) with the distance varying between x = 0 and x = xmax. The value for function P is 0 at x ...
4
votes
3answers
307 views
Boundary value problem with a DiracDelta
It seems that Mathematica can solve an initial value problem with a DiracDelta, but not a boundary value problem with a ...
1
vote
1answer
112 views
Boundary conditions at infinity for 1+2D wave equation in Mathematica 7
To solve a waves equation, I need to define some boundary conditions. The wave is propagating on an infinite plane, and it's not a membrane fixed on some fixed support. I'm have difficulties in ...
2
votes
2answers
594 views
Three coupled PDEs to be solved semi-analytically/analytically
I have been trying to solve the following three coupled PDEs where the final objective is to find the distributions $\theta_h, \theta_c$ and $\theta_w$:
$x\in[0,1]$ and $y\in[0,1]$
$$\frac{\partial \...
0
votes
0answers
38 views
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
...
0
votes
1answer
48 views
Give NeumannValue a nonlinear function
I have the following simpler example of my actual problem which reproduces my question
...
3
votes
1answer
137 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 ...
0
votes
1answer
76 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 ā a generalization of the logistic equation. In this case, the equation possesses a power-law ...
2
votes
2answers
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:
...
1
vote
0answers
173 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 bvp, there is solution given in output which is the solution from mathematica version 10.0.1.
Output from above in mathematica 10.0.1 is,
But when the similar ...
0
votes
0answers
113 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}$, ...
2
votes
0answers
149 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}}^{...
7
votes
3answers
595 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 ...
1
vote
0answers
91 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),$$
where $A,B,\sigma,r,b$ are constants and $g(t)$ ...
4
votes
3answers
248 views
Geometrically nonlinear beam deflection
Edit only for those interested in large deflections of beams
I discovered a mistake in the equations of the original question (below): in the normal force (compression/traction) ...
0
votes
2answers
98 views
Error when using NDSolveValue. Lists are not the same shape
Please, help me with the following issue.
I am solving the following system of the coupled PDEs
with the following boundary conditions
and initial conditions.
After performing the following ...
1
vote
0answers
58 views
NDsolve Boundary Condition is a Function of the Solution
I am trying to solve something like Fick's Law using NDSolve:
$$\frac{\partial \varphi}{\partial t}=\frac{\partial^2 \varphi}{\partial r^2}+F(r,t)$$
Subject to a ...
3
votes
1answer
97 views
Shooting Method with extra Unknown Condition
I've been trying to solve a system of 3 coupled 2nd order ODEs, for a real variable $x$, $0\geq x\leq \infty$. The equations are the following:
\begin{align}
&x^{2}\,h''(x) - x\,h'(x) + x^{2}\,g^{...
0
votes
0answers
69 views
solving a 2D eigenvalue problem for a partial differential equation
I'm fairly new to Mathematica and I'm looking for a way to solve a partial differential equation subject to periodic boundary conditions. The form of the equation looks like this:
$\frac{\partial^2}{\...
0
votes
0answers
41 views
Using NIntegrate/Integrate as boundary condition inside NDSolve
I try to implement a population model with age structure in Mma12 using NDSolve to get a numerical solution for my PDE. However, one boundary condition involves an integral, which gives me problems (...
2
votes
0answers
62 views
DSolve[] and initial conditions
Take some simple function of 2 variables, e.g. f[x_,y_] := x+y and try to solve a PDE of it for the general solution:
...
1
vote
1answer
97 views
Asymptotic boundary conditions for differential equation
I am trying to solve the following equation ($\ell\in \mathbb{N}$)
$$f''(x)+\left(1-\dfrac{\ell(\ell+1)}{x^2}+\frac{2}{x}\right)f(x)=0,$$
with these two asymptotic boundary conditions (b.c.) on the ...
0
votes
0answers
107 views
Analytical Solution to Laplace over Irregular Domain using DSolve
I would like to find an analytical solution to a Laplace equation over the following irregular domain using a mix of Dirichlet and Neumann boundary conditions. I've spent a lot of time trying to use ...
2
votes
1answer
133 views
Half-absorbing boundary conditions
I'm trying to solve the spherically symmetric wave equation
$$0 = (\partial_t^2 - \partial_r^2 + 1)\phi(t,r)\,,$$
where $\phi(t,0) = 0$. Without doing anything fancy, we can solve this equation "...
3
votes
1answer
151 views
Stiff System of ODEs: NDSolve Convergence Issues
I have tried to use NDSolve for solving 4th order coupled ODEs problems (see the attached codes). The MMA solver fails to solve this problem.
...
2
votes
1answer
129 views
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
...
4
votes
1answer
81 views
Periodic extrapolation out of the domain of the solution of a PDE in two directions
As a prototypic problem
...
asked Jul 25 '20 at 7:07
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8,4923 gold badges15 silver badges36 bronze badges
8
votes
2answers
1k 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 ...
2
votes
2answers
162 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 ...
1
vote
0answers
37 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 ...
8
votes
2answers
282 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 ...
4
votes
2answers
264 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.
...
