Linked Questions
15 questions linked to/from Variation of heat equation with guessed initial condition
54
votes
4
answers
8k
views
Dynamic Euler–Bernoulli beam equation
I am trying to solve for the vibration of a Euler–Bernoulli beam. The equation is
$\frac{\partial ^2u(t,x)}{\partial t^2}+\frac{\partial ^4u(t,x)}{\partial x^4}=0$
For the boundary conditions I ...
- 16.8k
18
votes
2
answers
5k
views
What's behind Method -> {"EquationSimplification" -> "Residual"}
In order to solve a quite large system of differential equations, I have the habit to use the NDSolve command without changing any options.
As I wanted more ...
- 970
15
votes
2
answers
1k
views
Solving Cahn-Hilliard equation: LinearSolve: Linear equation encountered that has no solution
I have built the Cahn-Hilliard Eqs. in MMA (Mixed Formulation, second order), However, it doesnot work in MMA using Finite Element.
LinearSolve: Linear equation encountered that has no solution.
And &...
- 1,864
14
votes
1
answer
1k
views
Why does NDSolve fail to solve the PDEs and spit out mconly warning?
I try to solve two coupled PDEs with NDSolve using the following code:
Set two operators:
...
- 189
7
votes
2
answers
192
views
ComplexExpand no longer assumes Derivative[__][__][__] as real
Bug introduced after 12.0.1, in or before 12.3, persisting through 13.0. Fixed in 13.2.0 or earlier.
Consider the following sample:
...
- 68.4k
11
votes
1
answer
871
views
Solve PDEs with finite difference scheme by modifying NDSolve-based solver
Motivation
As discussed here, NDSolve uses different difference orders for various spatial derivatives and the implicit design could cause trouble in certain cases....
- 643
7
votes
1
answer
917
views
NDSolve eigenvalue problem of bound state
I am trying to solve this eigenvalue problem:
\begin{align}
\mu \Psi(r) & =
-\frac{1}{2}\left ( \Psi^{\prime \prime}(r) + \frac{2}{r} \Psi' (r)\right )
-4\pi \Psi(r) \int _0^\infty dr' r'^2 \frac{...
- 393
5
votes
1
answer
736
views
WorkingPrecision in NDSolve causes failure when solving a simple PDE
I have fivefold multiple integral and I wanted a speed calculations. I came across on this Question and had already begun the problems.
Here is a toy example with simple double integral:
...
- 16.4k
1
vote
1
answer
335
views
Solve PDE system with mixed parabolic–elliptic equations
I want to solve a mixed PDE Parabolic-Elliptic system,
subject to initial conditions u(x,y,0)=1 and v(x,y,0)=2-0.5 cos[(Pi x)/5].
The respective code version ...
- 1,335
2
votes
1
answer
394
views
NDSolve for Coupled Second Order PDEs
I have the following set of equations that I have reduced down from a larger third-order partial differential equation
$f(x,y,t) = p(x,y,t) - (x-y)\left(\frac{\partial}{\partial x} - \frac{\partial}{\...
- 107
3
votes
1
answer
284
views
Mathematica and IBVP mixing temporal and spatial derivatives
The following PDE's-system-solving code
...
- 103
3
votes
2
answers
116
views
Need more equations in PDEs by NDSolve? Bug of mma?
I am trying to solve set of pdes as below
...
- 149
1
vote
0
answers
379
views
PDE combined with ODE 1D
I try to solve the following system of PDE coupled with ODE:
$$\theta_t - a\theta_{xx} + b\kappa_a(\theta^4-\varphi)=0,$$
$$-\alpha\varphi_{xx} + \kappa_a(\varphi - \theta^4) = 0,$$
$$-a\theta_x + \...
- 181
1
vote
1
answer
133
views
Problem Encountered when Solving a System Consisting of Two PDEs and an ODE in a Semi-NDSolve-based Approach
This is a continuation for question 300522.
Firstly, I have changed the equation for $C_{2\text{b}}^* $ in my system. The updated $C_{2\text{b}}^* $ is expressed as below:
$$
\begin{equation}
C_{2\...
- 391
1
vote
0
answers
77
views
Unable to implement boundary conditions for a spherical wave equation coupled to a Laplace equation
I am having trouble setting up in Mathematica v 12.1 the following
system of coupled pdes on $r\in[0,10]$
$$ \left(\partial_t^2 - \frac{1}{r^2}\partial_r r^2 \partial_r \right) \theta(t,r) = -(1+2\Phi(...
- 471