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

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13
votes
2answers
781 views

Numerical partial derivative

For a one-variable numerical function, it's simple to calculate the derivative at a point with Derivative as Szabolcs has pointed out before: ...
13
votes
3answers
840 views

Strategies to avoid LessEqual::nord in NMinimize?

When using NMinimize on functions with complex intermediate expressions (but a real end result), quite often one gets the error ...
7
votes
1answer
791 views

Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
2
votes
1answer
2k 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 ...
15
votes
3answers
802 views

Can Mathematica Handle Open Intervals? Interval complements?

Open Intervals Following up on this question, I was wondering whether Mma can handle open intervals. For example, the union of the intervals, $$1<x<5$$ and $$5<x<8$$ should not ...
5
votes
1answer
136 views

Why does taking advantage of Listable change the results of a numerical computation slightly?

I have two variables: t0, and teta0. The first is computed using several nested sums, the second is computed taking advantage to ...
5
votes
1answer
564 views

Function to subdivide interval into n evenly-spaced points

[This post needs better tags than I could come up with. Edits to the tags would be particularly welcome.] I realize that it is trivial to define a function that takes an interval (i.e. two ...
4
votes
1answer
315 views

Is there a way to globally set when to treat a very small number as zero?

I understand that I can use Chop to force a very small number to be treated as 0 and can use ...
7
votes
1answer
344 views
5
votes
2answers
529 views

how to solve ODE with boundary at infinity

y''[x]-x y[x]==0 y[0]==AiryAi[0], y[infinity]==0 the analytic solution to this ODE is the Airy function y[x]=AiryAi[x] if I ...
4
votes
1answer
200 views

How do I get a list of digits for a number?

I have this 200 digit number where I want to get the IntegerDigits, but the decimal point is in the way. ...
4
votes
1answer
761 views

MaxSteps and Computing time issue for Solving Differential equation in Mathematica

When we solve differential equation numerically using NDSolve then sometimes we get error like NDSolve::mxst: Maximum steps reached According to Mathematica docs ...
3
votes
3answers
676 views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
1
vote
2answers
171 views

Mathematica can't minimize a function

Mathematica seems not to be able to minimize this univariate function over integer arguments, $r>2, r \in \mathbb{Z}$. ...
1
vote
2answers
533 views
0
votes
1answer
108 views

How can I obtain more significant digits? [closed]

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 ...
28
votes
1answer
850 views

Numerics with Mathematica

From time to time, I would like to use Mathematica purely numerically, e.g., plotting a function which is defined as an integral which cannot be solve analytically or a solution of a differential ...
39
votes
10answers
2k views

Can Mathematica propose an exact value based on an approximate one?

Sometimes, I use Mathematica to do some hypothesis on homeworks to make the question easier. For instance, when I have to compute big sums when $n\to\infty$ and Mathematica can't give the exact ...
21
votes
3answers
590 views

Computing polynomial eigenvalues in Mathematica

MATLAB offers a function polyeig for computing polynomial eigenvalues, which appear, for instance in quadratic eigenvalue problems (see here for some applications) such as: \begin{equation} ...
15
votes
1answer
1k views

2D Heat equation: inconsistent boundary and initial conditions

I'm attempting to use NDSolve on a 2D boundary value problem with initial conditions. Upon running my code, I get the following message: "NDSolve::ibcinc: Warning: Boundary and initial conditions are ...
13
votes
1answer
487 views

How to guarantee that NDSolve correctly detects abrupt changes in parameters?

When using NDSolve, I often have parameters that, in most of their domain, have a constant or null variation, but that suffer from abrupt variations on a very small ...
19
votes
1answer
207 views

BitShiftRight produces incorrect results in Version 10

With Mathematica 10 for Mac, BitShiftRight works properly on lists of up to 100000 numbers, but appears to give incorrect results when threaded over lists of 100001 ...
8
votes
1answer
1k views

Minimization by Nelder-Mead

Finding a global minimum for this problem (non-linear optimization by the Nelder-Mead downhill simplex method) may not be possible, but by finding local minimum, I am expecting the value of the ...
6
votes
3answers
270 views
7
votes
1answer
664 views

What are the algorithm details of FindRoot?

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system". But I ...
3
votes
1answer
559 views

Monitoring the Evaluation of NDSolve: time to finish estimation

My problem is quite simple: I run a NDSolve with a system of many ODEs, a calculation that will run for many hours, and I would like to know the progress of the ...
12
votes
1answer
870 views

Numerical solution of coupled ODEs with boundary conditions

I have to solve the following set of ODEs and just can't get good results using Mathematica $$ r\frac{d}{dr}\left(\frac{1}{r}\frac{d}{dr}A(r)\right)-\xi^2F(r)^2\left(A(r)-1\right)=0 $$ $$ ...
10
votes
2answers
348 views

Determining the default Method used in optimization and root-finding algorithms

Is it possible to extract the Method which is used in functions like NMinimize, FindRoot, ...
5
votes
1answer
92 views

How to enforce numerical precision throughout a package

I developed a big package that does quite a bit of numerics. Is there a way to enforce that all numerical computations are done with a pre-defined accuracy? For example, can one use something like ...
5
votes
1answer
676 views

How can I get Mathematica to allow me to apply FindRoot to an expression that contains NIntegrate?

I am trying to run the following command in Mathematica: FindRoot[NIntegrate[D[f[x], x] / Sqrt[1 - x^2], {x, 0, 1}] - d, {a, 245}] As you might expect, a is ...
4
votes
1answer
130 views

NDSolve - sampling for result during the computation

I am using NDSolve for a Langevin dynamics problem. I want to the know long term behaviour of my system ($t>1$) but it has to be simulated with very small time steps ($dt\sim 10^{-9}$). An example ...
4
votes
2answers
472 views

Numeric calculation of Hessian

I want to calculate the Hessian matrix for a function that can only be evaluated numerically. So far, I have the following (where f is just for testing): ...
4
votes
3answers
320 views

How to cancel floating point factors?

I am currently having problems with some floating points. I have a function, which gives as an intermediate result (for example) ...
0
votes
1answer
250 views

How do I numerically solve a custom function?

Whenever I use functions like FindRoot or NDSolve, it sends x through the function and deals ...
14
votes
1answer
2k views

Parallelizing Numerical Integration in Mathematica

I have an ugly, six dimensional function that I need to integrate numerically. It works, but it currently take twelve hours to complete the calculation. Is there any good way to parallelize the ...
12
votes
4answers
378 views

Elegant high precision `log1p`?

Sometimes it is hard to understand how numerical expressions are evaluated. I remember reading claims by Wolfram on how smart the Kernel is to evaluate expressions trees numerically by recognizing ...
8
votes
4answers
320 views

Numerical instability in cosh and sinh - integral functions [duplicate]

I'm trying to calculate the function: CoshIntegral[x] Sinh[x] - Cosh[x] SinhIntegral[x] Unfortunately Mathematica seems to hit a point (x~20) and things become ...
8
votes
1answer
341 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 ...
8
votes
1answer
390 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 ...
5
votes
0answers
106 views

NMinimize seems to call function with the same values multiple times

I have to minimize a function where the evaluation of one parameter set takes very long (around 5sec) and discovered alongside, that NMinimize seems to call this ...
5
votes
3answers
839 views

Solution for equation system with piece-wise defined functions

As I could swear this worked just yesterday, I am probably just doing something stupid here and I am sorry to bother you :) I am trying to find the point where a curve crosses a line. In this case, ...
4
votes
3answers
746 views

Creating a 3D List Line Plot From Discrete Points

Given the following Runge-Kutta ODE solver and the graphical output below, how do I get a 3D line plot instead of a 3D point plot? I see that there is no ListLinePlot3D function, so I thought it might ...
4
votes
1answer
183 views

Find lengths of contours in a ContourPlot

I am trying to find the lengths of different contours in the following plot: It is a complicated piecewise function evaluated on the unit disk. I am hoping there is an easy, generalized way to ...
4
votes
0answers
406 views

Semidefinite Programming

I want to solve a numerical optimization problem using semi-definite programming. Is there a package or add-on that equips mathematica with this functionality?
3
votes
2answers
155 views

How to define even permutations correctly?

I define even permutations as following, but there may be some error. I use it in two different way and get different output. ...
3
votes
1answer
1k views

NDSolve does not respond

For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
2
votes
2answers
74 views

How to prevent Round with hided fractions

I found a strange behavior in Round. If we try: ToString[Round[4.811, 0.01], InputForm] we get: 4.8100000000000005 When I expected 4.81 In order to ...
2
votes
1answer
186 views

Area between Contours in ContourPlot

I feel slightly foolish for asking this because I am so close, but I'm having trouble, so I will anyway. I asked this question two days ago regarding finding the lengths of contours. Now, I'd like to ...
2
votes
2answers
275 views

Can Mathematica identify formulae or sequences of numbers?

Can Mathematica suggest what a formula means? For example if I input $$\sum_{i=0}^n i$$ can it infer that this is a sum of integer values from $0$ to $n$? Or if I enter $0,1,1,2,3,5,8,13$, can ...
2
votes
1answer
248 views

How to make Mathematica try harder to perform symbolic comparisons?

(I suspect this question is a duplicate, but I didn't find a sufficiently similar question with an answer to it.) I'm having trouble with comparisons of symbolic ...