# Tag Info

### Test a wooden board's vibration mode

The only reason I am attempting to answer this is to perhaps get a Reversal badge. There you go... We will go slowly and this answer is the basis for what comes next. Let's start with two dimensions. ...
• 36.1k
Accepted

### Numerical integration --- Mathematica vs Python (w/ Scipy) performance

General comments First, if you plan to use multi-dimensional integrals it is better to test with multi-dimensional integrals not with one dimensional ones. One might think that the test in the ...
• 35.2k

### Determining which rule NIntegrate selects automatically

This question comes up often enough. See this discussion at community.wolfram.com : Integration method used in NIntegrate , and the notebook Finding the applied NIntegrate methods attached to my ...
• 35.2k
Accepted

### Gillespie Stochastic Simulation Algorithm

Yes you can. Below is a fairly general, Mathematica-compiled, fast and robust version. Examples 1. Michaelis-Menten kinetics Michaelis-Menten kinetics for enzyme-directed substrate conversion. The ...
• 45.3k
Accepted

### How to implement custom integration rules for use by NIntegrate?

The simplest way to make new NIntegrate algorithms is by user defined integration rules. Below are given examples using a simple rule (the Simpson rule) and how <...
• 35.2k
Accepted

### Implement fractional Laplacian

I can provide an approach by finite elements and an application of the functional calculus of selfadjoint operators. Background The spectrum of the Laplacian on a bounded domain $\varOmega$ with ...
• 95.6k

### Nonlinear differential equation: numerical solution

Introduction I think there are several questions on this site about ODEs of the form $$(x-a)^2 u''(x) = F(x,u,u')$$ with an initial condition at $x=a$. There is no general guarantee that solutions ...
• 217k

...
• 8,487
Accepted

### What's behind Method -> {"EquationSimplification" -> "Residual"}

This post contains several code blocks, you can copy them easily with the help of importCode. As mentioned in the comment above, the answer is hidden in this ...
• 52.8k
Accepted

### Easy way to plot ODE solutions from NDSolve?

I wanted to share some undocumented techniques that give quick rough plots of NDSolve solutions. The keys points are this, the second one being quite handy at ...
• 217k
Accepted

### How do I create a triangulated surface from points?

It turns out ListSurfacePlot3D does a terribly poor job of approximating the surface in the OP, otherwise one will just apply ...
• 32.5k
Accepted

### How to implement custom NIntegrate integration strategies?

Motivation (for a new semi-symbolic integration strategy) Consider the following integral, which cannot be done neigther by Integrate: ...
• 35.2k
Accepted

### Numerically solve the initial value problem for the 1-D wave equation

I've waited for this question for a long time :) Fully NDSolve-based Numerical Solution There actually exist 2 issues here: NDSolve can't handle unsmooth i.c. ...
• 52.8k
Accepted

### Can Mathematica calculate this elliptic, triple integral?

Doing the Integrals separately for a, b and c gives the answer $\frac{128}{45 \pi}\sim 0.905415$, which agrees with the numerical estimate from NIntegrate: ...
• 974
Accepted

### Plotting a Bifurcation diagram

An alternative representation is ...
• 58.4k

### More efficient method to compute moments of the Johnson $S_B$ distribution

I'll preface this answer first with a complaint: NExpectation[] and NProbability[] are not sufficiently resilient obviously ...
Accepted

### Interpreting Mathematica code on black holes

I managed to debug the code from KerrOrbitGRProject and reproduce the results for the Schwarzschild metric (figures on pp. 7-8) ...
• 34.1k

### Boundary condition with spatial derivative is ignored by NDSolve

Short Answer Set Method -> {"MethodOfLines", "DifferentiateBoundaryConditions" -> {True, "ScaleFactor" -> 1}} inside ...
• 52.8k
Accepted

### 1D Euler equations (fluid dynamics) with NDSolve

Update-1: The initial conditions in the question were wrong/incomplete. (removed 1/0 errors) Update-2: The 1D Euler equations were modified to match this source. (ultimately not necessary in V10.4, ...
• 7,237

### Only final result from NDSolve

There is actually a somewhat cryptic but very simple way to make NDSolve only return the solution at the end point: ...
• 23.1k

### Mismatch between numerical and analytic evaluation of an integral

After a lengthy study (I'm using version 8) I conclude that there is a bug in Mathematica in the Integrate function when applied to a ...
• 12.8k
Accepted

### Obtaining an NIntegrate error estimate

From Anton Antonov's answer to Determining which rule NIntegrate selects automatically, we learn we can get the error estimate(s) using the undocumented option ...
• 217k
Accepted

### Plotting separatrices for nonlinear system

We can solve (approximately) for the initial conditions of solutions that approach an equilbrium by comparing the displacement vector from the equilibrium with the vector field of the ODE. Such ...
• 217k
Accepted

### Is there any possibility to implement a structure like a ProgressIndicator into NDSolve?

Here are a few versions I use: 1) ...
• 36.1k
Accepted

### Boundary sphere partial differential equation

The differential equation should reflect the fact that θ ranges between 0 and Pi. Because ...
• 58.4k

### How much time should one give Mathematica for an integral evaluation?

For what it's worth, you can monitor the progress of Integrate and NIntegrate. I'm not sure how helpful the tools below are, ...
• 217k

### NDSolve uses different difference order for different spatial derivative when solving PDE

Note: fix is broken since v11.3, a new question has been started aiming at upgrade it. Here's my approach for fixing the difference order. The key idea is ...
• 52.8k