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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...