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

learn more… | top users | synonyms (1)

2
votes
0answers
36 views

Problem solving a nonlinear partial differential diffusion equation

EDIT: actualy the nonlinear partial differential equations for interacting density distributions, including boundary conditions, should be given as $$ \frac{\partial\phi}{\partial t} = D ...
5
votes
2answers
78 views

A problem with Compile and Map

There is a weird behavior of Compile that I do not understand. Consider the following example: ...
7
votes
3answers
3k views

Does Mathematica get Pi wrong?

I happened to watch a Youtube video on Pi. According to the video, the 1 millionth digit of Pi is 1. And here is another page of the first 1 million digits of Pi. You can get the same answer from ...
0
votes
1answer
57 views

usage of random numbers in recursive loop

I am trying to evalute two functions using iterative process as below ...
2
votes
0answers
47 views

How to speed up solution of system of recurrence equations

I was wondering how I can improve the speed on this method for solving a particular system of coupled recurrence equations. The system is $$ \begin{align*} &V(m)=\alpha + \beta V(m+1)+\beta ...
-2
votes
1answer
54 views

How to generate normally distributed random number [closed]

I want to sample or return random number from a distribution which is normally distributed with mean of zero and standard deviation of 1. I am using RandomReal[NormalDistribution[0, 1]] I s this ...
-2
votes
1answer
88 views

Why does Mathematica “sleep” when I don't work at computer? [closed]

I started using Mathematica few days ago. I'm running this code: ...
0
votes
1answer
62 views

numerically solving

I am trying to solve for [Lambda] as a function of a (unknown) from this expression ...
0
votes
0answers
37 views

Second derivative using ND [duplicate]

I have a function g=f(x,t). The function "g" came from a numerical integration: g[x_?NumericQ,t_?NumericQ]:=NIntegrate[tt[x,r,t],{r,rmin,rmax}] and tt(x,r,t) ...
1
vote
1answer
46 views

Imaginary terms in the derivative of Jacobi theta function (2) on the real line

I am trying to calculate/plot the derivative of the second Jacobi theta function $d\theta_2(0, e^{-\pi t} )/dt$. Calculating or plotting the function itself works fine: ...
2
votes
0answers
30 views

How do I numerically integrate over a data set that has uncertainties? [closed]

I have a 1D data set {xi, yi} with no uncertainties in xi and with uncertainties dyi in yi. The resulting discrete function is monotonic and relatively smooth and I would like to integrate the ...
3
votes
1answer
86 views

compute the gradient in high dimension

The following code is used to compute the gradient of a given 2D data. ...
0
votes
0answers
39 views

Integro differential eq boundary difficulties

I'm trying numericaly solve simple integro-differential equation, but have some problems with boundary conditions. System: ...
0
votes
1answer
62 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
90 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
25 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 ...
0
votes
0answers
29 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
90 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 ...
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
110 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 ...
1
vote
1answer
107 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
35 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
1answer
92 views

Define and refine mesh around a hole

I am solving Laplace equation with particular geometry and boundary conditions: ...
0
votes
1answer
77 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 ...
3
votes
2answers
160 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. ...
0
votes
0answers
45 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 ...
4
votes
4answers
268 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: ...
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
66 views
2
votes
2answers
121 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 ...
0
votes
1answer
71 views

Numerical integration and plotting

New to Mathematica, and trying to numerically evaluate two integrals: ...
2
votes
2answers
154 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
104 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 ...
1
vote
1answer
146 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 ...
4
votes
4answers
149 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: ...
0
votes
0answers
36 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
70 views

Fixed Points Problem with 2D Mapping

I have been playing with the mapping given by ...
0
votes
0answers
37 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
99 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
55 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
225 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 ...
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} ...
3
votes
2answers
66 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
39 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 ...
1
vote
2answers
76 views

Performance in calculating maximum-likelihood- based estimates

My probability density function is a complicated one for which numerical estimation is necessary. Here my pdf: ...
4
votes
1answer
85 views

FindFit runs extremely slow for my Function,how do I optimize this?

My function is the first order Bessel Function, and I am basically just trying to get this to fit in a way that does not take forever. I define the function as follows, (it seems to work faster if I ...
0
votes
1answer
37 views

How to force numeric evaluation?

I need to evaluate the PolyLog function at some points, but I'm interested in numeric values. E.g. PolyLog[3, 2.7] works fine, but PolyLog[3, e] just prints the same PolyLog[3, e]. I somehow need to ...
9
votes
2answers
209 views

Solve a PDE over a region defined by a Bezier patch

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