Linked Questions

46 votes
4 answers
6k 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 ...
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  • 14.8k
17 votes
2 answers
4k 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 ...
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  • 890
12 votes
2 answers
891 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 ...
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  • 1,746
14 votes
1 answer
933 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: ...
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  • 899
11 votes
1 answer
691 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....
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  • 661
7 votes
1 answer
726 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{...
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5 votes
1 answer
515 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: ...
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1 vote
1 answer
257 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 ...
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  • 1,100
4 votes
2 answers
91 views

ComplexExpand no longer assumes Derivative[__][__][__] as real

Bug introduced after 11.3, in or before 12.3, persisting through 13.0. Consider the following sample: {Re, Im}[u'[t]] // Through // ComplexExpand In v9.0.1 ...
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  • 52.3k
1 vote
1 answer
336 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}{\...
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3 votes
1 answer
210 views

Mathematica and IBVP mixing temporal and spatial derivatives

The following PDE's-system-solving code ...
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  • 93
3 votes
2 answers
111 views

Need more equations in PDEs by NDSolve? Bug of mma?

I am trying to solve set of pdes as below ...
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  • 103
0 votes
0 answers
344 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 + \...
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1 vote
0 answers
66 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(...
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  • 367