Questions tagged [boundary-conditions]

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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{\...
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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 ...
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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 (...
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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 ...
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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
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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 $\boldsymbol{r}\left(s\right)=\left(x\left(s\right),y\left(s\right)\right)$ ...
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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 ...
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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. ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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. ...
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91 views
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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 \; \...
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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: ...
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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 ...
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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 ...
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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 ...
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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
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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 \...
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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 ...
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1answer
48 views

Give NeumannValue a nonlinear function

I have the following simpler example of my actual problem which reproduces my question ...
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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 ...
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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 — a generalization of the logistic equation. In this case, the equation possesses a power-law ...
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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: ...
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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 ...
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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
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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
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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 ...
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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 $g(t)$ ...
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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) ...
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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 ...
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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 ...
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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^{...
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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
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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 (...
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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: ...
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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 ...
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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
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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
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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
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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 ...
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1answer
81 views
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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
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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 ...
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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
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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
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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. ...