# Questions tagged [numerics]

Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.

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I'm trying to reproduce the following plots: As described by this blog entry: Synchrotron radiation As you can see in the linked article, the task is essentially to make a ...
2k views

### Why can't I change the value of MaxRecursion in NIntegrate when integrating BesselJ?

Bug introduced in 8.0.4 or earlier and persisting through 11.0.1 or later I am trying to evaluate this integral numerically $$\int_0^{\infty } J_0(q R) \tanh(q) \, \mathrm{d}q$$ for large values ...
639 views

### Preventing Numerical value from being evaluated

I have searched stackoverflow (and comparable pages) for quite a while now (got redirected from there to this specialized stack), and I surrender. I am trying to evaluate an expression that is small ...
984 views

### NDSolve and memory usage

After some googling, i've found similar problems around, but didn't find a 100% satisfactory answer, so let me ask here: I'd like to solve a 1+1 problem using the method of lines. In spherical ...
486 views

### Function for a series of joined slopes

I need a function for a series of joined slopes and my solution feels a bit kludgy. Is there a better way? A list of pairs of transition points and slopes: ...
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### How to find the next root larger than a specified value, numerically?

I would want to have a general-purpose, reasonably robust method of finding the next numerical root above a specific value of x. I'm stumped by the fact ...
852 views

### FEM: Nicer Element Shape for Spherical Region

I'm trying to generate a mesh for later use in the Finite Element Method of the DSolve command. It is basically a parallelepiped with a spherical indentation. I'm ...
689 views

### Understanding simple numerical calculation

I am trying to understand why N[0.1]//FullForm returns 0.1' (A). Indeed, $0.1$ in base two is $0.000110011001100110011...$. If I ...
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### Nonlinear dispersal equation modeling insect aggregation

I'm a newbie with Mathematica, I know it's a basic answer, but I can't solve the problem on my own. I have the following equation reflecting insect aggregation at low population densities (taken from ...
679 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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### Dr. StrangeNumbers or: How I Learned to Stop Worrying and Love Floating Point Arithmetic

The following is the program. ...
409 views

### Fast pairwise SameQ test of an ordered list

I have an ordered list of $N$ numbers, and I want to find out whether adjacent numbers are SameQ or not, returning a list of 0s and 1s of length $N-1$. One approach ...
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### Mod[1.2, 0.2] is not equal to zero

Why doesn't the following expression evaluate to zero? In:=Mod[1.2, 0.2] Out=0.2 Edit: This is what I wanted to do: ...
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### Wonky Solutions to Schrödinger Equation with Box Barrier

I'm trying to solve the Schrödinger equation using NDSolve in a case where there is a potential box barrier. The initial condition is a cosine wave, and for ...
460 views

### Numerically solving Helmholtz equation in 2D for a Guitar

Hi I am new to using Mathematica, so am not too confident. I am essentially trying to model vibrations of a guitar sound board for a project. It would be great to get some visualisations of the ...
4k views

### How to solve fluid flow problem based on Navier-Stokes equations? [duplicate]

Does anyone know or can provide any examples how fluid flow problem can be formulated and solved in Wolfram Language? Simplest cases of 1D or 2D flows based on Navier-Stokes equations or even their ...
658 views

### Solve a PDE over a region defined by a Bézier patch

I am using NDSolve to find the solution to a PDE over an arbitrary domain. The domain is specified by a Bézier patch. ...
383 views

### Vastly incorrect answers obtained by increasing WorkingPrecision with modified Bessel functions

Bug introduced in 7.0 or earlier and fixed in 11.0 This is a follow-up to this question regarding numerical instabilities occurring with modified Bessel functions. In trying to explore J.M.'s answer ...
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### What are the hidden specifications for FindRoot

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system" (or a nonlinear equation I suppose). ...
691 views

### Converting other C++ classes to MTensor in LibraryLink

Hopefully this will be a quick question + a quick answer: Say I have a C++ (or C) code using LibraryLink. I am using a library that defines a specific matrix class, as many numerical libraries ...
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### Why does NMaximize miss this global maximum?

I am having trouble maximizing a function which appears as a curvature of a planar curve. ...
910 views

### Distances between points in periodic cube

Question How can one implement more efficiently/elegantly/memory savvily the following function which returns a matrix of all Euclidian distances between points in 3D within a cube of width ...
1k views

### Why does N[1.000 01, 10] return 1.00001, but N[1.000 001, 10] returns only 1.?

Why is it so? When I ask for N[1.00001, 10] I get quite reasonably 1.00001 But when I ask for ...
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### Morphing between two functions

Assume we have 2 peaked positive functions f[x_] := Exp[-(x + 3)^2] g[x_] := 1/2 Exp[-(x - 3)^2/4] that look like Would it be possible to numerically find a ...
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### Why is Mathematica destroying this graph?

Here I have a picture of a function I graphed: reg[x_,y_]:=(x^2+y^2)Cos[4ArcTan[y/x]]; Plot3D[reg[x,y],{x,-2,2},{y,-2,2},AxesLabel->Automatic] And here is ...
984 views

### What is the fastest way to compute digits of $\pi$ using Mathematica?

There are a lot of ways to calculate digits of $\pi$ using Mathematica. The most naïve way I can think of is N[π, 100000000] Of course, there are a lot of fast ...
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### Demonstrating the behavior of a function as its independent variable approaches zero

I have several questions regarding the function $$f(x)=\frac{\sqrt{x^2+9}-3}{x^2}$$ that I would like to help my students with in the upcoming semester. Now, the limit as $x\to 0$ is 1/6. ...
546 views

### Wrong results from NSolve on coupled polynomials. WorkingPrecision -> Automatic fails

OP UPDATE: I received an email from WR on 1-18-2016: "...It does appear that the NSolve function is not behaving properly in this case and I have forwarded an incident report to our developers with ...
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### Kernel quits without error in NDSolveValue

The crash is fixed in version 10.3 I am using the latest 10.1. The following single line command makes the kernel quit without error message (just a beep): ...
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### Solving a linear system with a badly conditioned matrix

My question is related to this one: Badly conditioned matrix (General::luc) I'm trying to solve a linear system of the form A.x=b. As suggested in the referenced post since I'm not really interested ...
4k views

### Nonlinear PDE solver

I would like to solve the following nonlinear PDE: $$\frac{\partial^2 \phi}{\partial x^2} - \frac{\partial^2 \phi}{\partial t^2} = \lambda |\phi|^2 \phi$$ I was trying: ...
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### Problem with numerical evaluation of analytically solved integral, solution way off

The following command in Version 9.0.1: N[Integrate[x^50*Sin[x], {x, 0, 1}]] gives $1.4615\times 10^{48}$ which is way off from the correct solution which is ...
2k views

### Numerical integration of a numeric data available as a nested list

I have some numerical data in the form of a list with the following structure: {...{x,y,z},...} defining a surface z=z(x,y) in a 3D space (x,y,z). The data came from a simulation, and I am post-...
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### Fitting experimental data by using ParametricNDSolveValue and NonlinearModelFit

I am a newcomer to Mathematica. Basically I just want to fit the data (enzyme kinetic data) shown below to a system of odes' by using NonlinearModelFit. The data, an 101x2 array, contains time in the ...
10k views

### Forcing FindRoot to return only real solutions

FindRoot documentation reports that if the equation and the initial point are reals, the solutions are searched in the real domain. However, in the following case I ...
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### Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
623 views

### Confused by (apparent) inconsistent precision

$$e^{\pi \sqrt{163}} \approx 262537412640768743.99999999999925$$ E^(Pi Sqrt[163.0]) N[E^(Pi Sqrt[163.0]), 35] NumberForm[E^(Pi Sqrt[163.]), 35] returns <...
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### Finding self-intersections of a closed curve represented by an interpolation function

I've been trying to find particular simple closed curves on a plane. ...
1k views

### Nonlinear ODE eigenvalue problem

How does one find eigenvalues $\lambda$ of the following problem? $$\frac{\mathrm{d}^2 u}{\mathrm{d}x^2} = \lambda \left( -u + u^2 \right),$$ $$u(0) = u(1) = 0.$$ Can this be tackled by ...
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### Symbolic Integration along contour: branch cut problem?

Context Following this question on path integrals in the complex plane, having defined again a numerical and symbolic integrator along a path as ...
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### The numerics of FresnelS[]

Bug introduced in 12.1 or earlier and persisting through 12.1.1 or later [CASE:4615361] Note: A worse problem existed in 12.0 for inputs greater than 8 and of ...
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### Evaluating Lauricella functions in Mathematica?

Consider the Lauricella functions. The Mathematica documentation does not contain anything regarding Lauricella. Is there any known way (e.g. an unofficial package) ...
292 views

### Integration of Booles and Gaussians in high dimensions

Context As a follow up of this question, I would like to predict the connectivity of the so-called cosmic web in arbitrary dimensions. The connectivity $\kappa$ is defined as the number of ridges ...
838 views

### Circumvent NDSolve::bdord: error for 1-D Euler Equations

I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a non-...
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### Does Overflow[] poison session for N?

Summary: once Mathematica hits an overflow error, N[] appears to break for even simple calculations. RealDigits[N[Sqrt-1,10^8]]; I was impressed that ...
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### How to modify NDSolve`StateData without crashing the kernel?

Probably a hard question, but it's better to cry out loud. Reminded by Chris K, I noticed my fix function has been broken since v11.3. After some checking, I ...
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### A problem about function N

Toady,I have a problem about N,described as below: For example N[1/3, 5] (* ==> 0.33333*) and ...
894 views

### Complex result for Real vectors in VectorAngle

I was expecting a real angle using VectorAngle when passing real valued vectors, but I obtained a complex angle: ...