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

learn more… | top users | synonyms (1)

4
votes
2answers
134 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
110 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
183 views

compute the gradient in high dimension

The following code is used to compute the gradient of a given 2D data. ...
3
votes
1answer
108 views

Why is the Spherical Bessel Function acting strangely at this point?

I'm doing some computation that requires the use of Spherical Bessel Functions of the 1st kind, at high orders and values. So, I managed to find this, while running it over a wide range of values. I ...
0
votes
0answers
61 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
75 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
138 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 ...
0
votes
0answers
39 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
222 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
79 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
164 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 \binom{m}{i}\binom{...
1
vote
1answer
160 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
473 views

Laplace PDE in a polar coordinate system

I want to solve a Laplace PDE in a polar coordinate system with finite difference method, but I have a problem with boundary conditions at r = 0. Here is what I ...
3
votes
1answer
179 views

Define and refine mesh around a hole

I am solving Laplace equation with particular geometry and boundary conditions: ...
0
votes
1answer
98 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 ...
5
votes
2answers
318 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
83 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 ...
1
vote
1answer
68 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
57 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
115 views
2
votes
2answers
360 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
233 views

Numerical integration and plotting

New to Mathematica, and trying to numerically evaluate two integrals: ...
3
votes
2answers
198 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
136 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
282 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 ...
19
votes
2answers
608 views

Different floating-point numbers equal?

Let's define two different numbers. x = 1. y = 1. + 2^-52 (* equivalently, 1 + $MachineEpsilon *) Let's make sure they're different with ...
4
votes
4answers
279 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: ...
1
vote
1answer
41 views

Generation of list of values for small gap among values

I need to run a loop as Table[expr,{i,imin,imax,di}] where I want di to be as small as order of ...
2
votes
1answer
146 views

Fixed Points Problem with 2D Mapping

I have been playing with the mapping given by ...
0
votes
0answers
74 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
142 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
106 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) ...
8
votes
1answer
438 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
104 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
96 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
58 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 \frac{1}{2}-A,\frac{1}{2}-A,\frac{1}{2}-...
1
vote
2answers
110 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
116 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
297 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, ...
9
votes
2answers
370 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. ...
11
votes
1answer
352 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: ...
1
vote
1answer
206 views

NSolve on bounded domain

I don't expect NSolve[] to be able to obtain all solutions in generalfor example. In principle there should be an algorithm that finds all solution to $f(x)=0$ for $...
8
votes
1answer
221 views

Numerical Integration different in Mathematica version 9 and 10 with same options

I have noted that the same function with the same settings gives me different results in Mathematica version 9 and 10. This involves integrating numerically interpolating functions and so on. Here a ...
0
votes
2answers
125 views

Derivative after numerical Integration

So I have a function that I want to numerically integrate with respect to temperature, so the integral changes depending on the value of temperature being used as it is one of the bounds. After ...
1
vote
1answer
62 views

Characterising the set of parameters that satisfy a system of non-linear equations

I am looking for a solution to the following problem and could not find an answer so far. I have a quintic equation, $f(x;a,b,c,\cdots)-x=0$, where $x$ is the variable with respect to which I need the ...
0
votes
2answers
156 views

Accuracy and WorkingPrecision

Observe that ...
-1
votes
1answer
80 views

My code of plotting a two-variable function is too slow [closed]

I have a code in which my complicated function to be plotted is F(x,p). I would like to graph it for 5 values of p equal to 10^7, 10^8, 10^9, 10^10 and 10^11 for x values between 0.01 and 0.99. All ...
0
votes
1answer
529 views

Problem with FindRoot applied to functions

I am having difficulty with the error "is not a list of numbers with dimensions..." when using FindRoot (and other numerical routines in Mathematica) to solve equations numerically when the argument ...
1
vote
1answer
118 views

Wrong generalized eigenvalues of large numeric matrices

I've been working on a toy model of a variational method of a Hamiltonian H with an overlap matrix S. The point is that when H and S are small enough, Mathematica gives the correct eigenvalues (≈ -1,-...