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

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3
votes
1answer
67 views

compute the gradient in high dimension

The following code is used to compute the gradient of a given 2D data. ...
74
votes
1answer
1k views

Why are numeric division and subtraction not handled better in Mathematica?

There is something that has been troubling me for a while. At least through version 10.0 the performance of a / b and a - b is ...
0
votes
0answers
36 views

Integro differential eq boundary difficulties

I'm trying numericaly solve simple integro-differential equation, but have some problems with boundary conditions. System: ...
14
votes
2answers
171 views

CompiledFunction returns machine numbers smaller than $MinMachineNumber

When thinking on the workaround for this LogLogPlot bug suggested by halirutan I noticed that CompiledFunction actually can ...
0
votes
1answer
58 views

Why does Compile redo the calculation when overflow happens?

When implementing the Numerov method solving Schrodinger equation, I encountered this problem. In order to show the order of the evaluation, Print is added. ...
0
votes
1answer
80 views

How to adjust excel data for NonlinearModelFit?

I'm really new to Mathematica and I'm facing a problem and would really appreciate some help! Maybe my question is similar to one described in How to fit 3 data sets to a model of 4 differential ...
-1
votes
0answers
23 views

How could I speed up a code including a Module with many functions

I have implemented a big formula through the mathematica function Module. Within this module a lot of definitions are made (i.e. function[x_]:=). The code are working well but it is too slow. I am ...
10
votes
4answers
3k views

How can I differentiate Numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
0
votes
0answers
26 views

How to use FindFit to find the parameter in Laplace space(numerically inverting Laplace transforms)

I am trying to find the parameter in Laplace space, and a very simple example is shown below: I have known the solution $y_{laplace}$ in the laplace space is $a/s^2$, and I also have some discrete ...
0
votes
2answers
82 views

Numerical 3D Integration in Mathematica [closed]

My question in short is: Is it possible to make numerical 3D integration in mathematica efficiently? Or am I gonna have to move this to C++? I feel this problem is way too trivial to go to C++, so ...
24
votes
2answers
892 views

Funny behaviour when plotting a polynomial of high degree and large coefficients

I am trying to plot a polynomial of degree 29 on the domain [0,1], with fairly large coefficients: ...
36
votes
6answers
6k views

Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)

Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$. When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], Mathematica gives the ...
0
votes
0answers
57 views

Optimising prime number test code

Is it possible to speed-up this code ? Also, It would be great if people could test this algorithm. I only have a Raspberry Pi to test it on, so I can't be certain it's not a strong probable prime ...
0
votes
2answers
107 views

Compute expectation numerically

I want to compute this expectation numerically with Mathematica. I could not figure out how to solve it numerically. Could you please help me? $$E(x|p)=\sum _{i=0}^m \sum _{j=0}^m ...
26
votes
1answer
833 views

Fast Spherical Harmonics radiative transfer

This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me. I am using ...
1
vote
1answer
77 views

NIntegrate over a list of functions

This question is the result of these other two questions. Question 1 and 2. I thought it would be better to ask a new question rather than deleting previous one. I think When ...
10
votes
1answer
572 views

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

Bug introduced in 8.0.4 or earlier and persists through 10.0.2. I am trying to evaluate this integral numerically $$ \int_0^{\infty } J_0(q R) \tanh(q) \, \mathrm{d}q $$ for large values of $R$. ...
1
vote
1answer
100 views

Poisson PDE in a rectangular domain

I found a solution for this problem, but this is in Scilab and I never use Scilab. Can anyone can help me to translate it in Mathematica? Here is the Link:http://imechanica.org/files/TorqueR.pdf I ...
0
votes
0answers
29 views

numerical integration with parameter

Now I'm trying to integrate a function numerically. But it shows always an error message. x=y is not a valid limit of integration I know that this function ...
3
votes
2answers
152 views

NDSolve in Mathematica won't use all the cores avaiable

When I solve a system of differential equations in Matlab, the task manager shows that all the CPU cores are in use. This is not true when I solve the same system in Mathematica. I have six cores. ...
3
votes
1answer
87 views

Define and refine mesh around a hole

I am solving Laplace equation with particular geometry and boundary conditions: ...
2
votes
2answers
217 views

How to solve this numerically?

May I ask what is the best way to evaluate ...
2
votes
2answers
101 views

WorkingPrecision causes issue in the NIntegrate

I really can't figure out why my code sometimes is not working. My integrals involve two variables (k and kz). The integration ...
0
votes
1answer
75 views

Floating point arithmetic bug caused by Table[]

I was doing something fairly ordinary and noticed something I can't, for the life of me, explain. For context, I wanted to take make a function that takes an array of data like the one below, then an ...
0
votes
0answers
43 views

Any way of solving this system of nonlinear equations with non integer powers?

I have a system of four nonlinear equations. Some of the exponents are fractions. I was wondering if this is what is causing NSolve to run for hours without giving ...
10
votes
1answer
377 views

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 ...
0
votes
1answer
132 views

How can I obtain more significant digits? [duplicate]

I type f1[x_] := 12 x^5 - 975 x^4 + 28000 x^3 - 345000 x^2 + 1800000 x N[f1[15.5], 15] and obtain 3.74112*10^6 BUT It´s not true!!! the result is larger than ...
0
votes
2answers
129 views

Spiral roots, how?

I found this picture on the net, as I can play in mathematica
1
vote
1answer
35 views

Implicit region is not “valid” in ParamatricNDSolveValue function?

I am trying to solve a geometric problem with relation to my Schrodinger equation and its boundaries. Here is my code: ...
0
votes
1answer
72 views

How to obtain a convergent solution iteratively for a linear system of equations

I am working on a problem that requires an iterative procedure to solve a linear system of equations, the system of equations in matrix form is: $$\underbrace{\begin{bmatrix} r_{11} & r_{12} ...
1
vote
1answer
46 views

Determine whether one value is divisible by another [closed]

How do I determine whether one number is evenly divisible by another in the case of large numbers, for example: 52^52 / 52!
1
vote
1answer
136 views

Slow evaluation of NIntegrate when used as a pure function

I asked a perhaps related question here. Here is my code in below. The goal is that to define a function which must be integrated numerically. The function itself first is calculated over different ...
0
votes
1answer
68 views

Numerical integration and plotting

New to Mathematica, and trying to numerically evaluate two integrals: ...
4
votes
4answers
147 views

First digit difference between two numbers

I was trying to build a function that finds the first decimal place difference between two decimal numbers of same sign. An example: ...
2
votes
2answers
153 views

Entropy of the elements of a general data set

I have the following data set, and wish to track the evolution of the entropy of each element within the set. I have evaluated the entropy for some elements, but how does one evaluate the entropy of ...
1
vote
1answer
101 views

Quantum Physics question [closed]

I'm not sure if anyone here would be able to help me. But if you know a more appropriate place where I could ask for help, please let me know. So here's the question: And here's my attempt at ...
3
votes
1answer
82 views

Why is left NumberPadding always applied in NumberForm?

I would like to display numbers like 9.0001 and 10.0001 in the fixed-width form of xx.xxxx. ...
0
votes
0answers
34 views

real eigenvalues, imaginary eigenvectors

Solving the most basic eigenvalue problem, the 1d Schrodinger equation in Mathematica can be tackled either through a ParametricNDSolveValue (which I don't like) or implementing a full numerical ...
2
votes
1answer
65 views
2
votes
3answers
144 views

Plot a bunch of lines in 3D from point data

I have a 12*25 array, wherein each entry is of the form $\{x,y,z\}$. So 12 different $x$ values, 25 different $y$ values and 12*15 $z$ values in all. I'd like to plot 12 curves of various $x$ values ...
1
vote
1answer
85 views

The problem (time) caused by ?NumericQ

In here, I asked a related (similar) question. Using ?NumericQ seems have slowed down the entire calculation. But I now have a more serious problem: ...
0
votes
0answers
36 views

NDSolve dependence on initial values

I'm checking some results in this paper and I'm currently having some issues with a numerical integration of a set of differential equations using NDSolve (section 2 and 3.1-3.2 in the paper). I'll ...
3
votes
2answers
96 views

Finding solutions at non-differentiable points of a numerical function

Let's consider a 2D function we can evaluate numerically, but which is opaque to symbolic manipulation (this is just an example): ...
0
votes
1answer
50 views

Numerical integration of a three dimensional array

I need to integrate a scalar valued function $f\left(\boldsymbol{x}\right)$ where $\boldsymbol{x}$ is a three dimensional position vector; in other words: $\int_{\Omega} f\left(\boldsymbol{x}\right) ...
6
votes
1answer
214 views

How trustworthy is NMaximize?

Suppose I solve a constrained optimisation problem using NMaximize. How confident can I be of the accuracy of the result? For concreteness, suppose that F,G are ...
3
votes
2answers
65 views

Slow application of `Outer` on a matrix

I have some performance issue with the calculation of a gaussian kernel applied to a not-that-large dataset. I'm not very good with performance tuning in Mma and I have the feeling this one could be ...
1
vote
0answers
38 views

Is it possible to circumvent this overflow?

I'm trying to evaluate the following function numerically: $ f(A,B)=\frac{2A\pi ^{5/2} (-1)^B}{(A!)^2B!} \, _4\tilde{F}_3\left({\frac{1}{2},1-A,1-A,1-B\atop ...
10
votes
1answer
260 views

Does NRoots own an abstract counterpart? If not, can we write one?

We know when solving linear algebra equations, despite its abstract syntax, LinearSolve is much faster compared to Solve: ...