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

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20
votes
2answers
234 views

BitShiftRight produces incorrect results in Version 10

fixed in 10.0.2 With Mathematica 10 for Mac, BitShiftRight works properly on lists of up to 100000 numbers, but appears to give incorrect results when threaded ...
17
votes
1answer
678 views

Dual complex integral over implicit path using contour plot

Context I am interested in doing double contour integral over paths which are defined implicitely. For the sake of debugging, let's assume its $$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
9
votes
1answer
974 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
808 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 ...
13
votes
1answer
1k 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
1answer
390 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 ...
5
votes
1answer
101 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 ...
4
votes
1answer
162 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
653 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
348 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
269 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 ...
13
votes
2answers
376 views

Why do NumberForm and Round apparently use different tie-breaking methods?

When rounding numbers (for example, rounding a real number to the nearest integer), the "round to nearest" rule is usually used. For example, 1.4 is rounded down to 1 and 1.6 is rounded up to 2. ...
8
votes
4answers
370 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
420 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 ...
6
votes
2answers
312 views

A problem about fixed point iteration theory

Description Recently, I have been learning a couse called "Numerical Analysis". The fixed point iteration theory was introducted to solve the ...
5
votes
0answers
124 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
1answer
917 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 ...
5
votes
3answers
977 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
1answer
224 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 ...
3
votes
2answers
112 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
2answers
246 views

How do I feed data points into an equation to solve NUMERICALLY?

I start with this equation and solve it numerically for $z(x,y)$ in the range $1 < x < 5$ and $1 < y < 5$: $$ \frac{3}{xyz} - 2x - 3y - 5z = 0 $$ Then using the data points of $z$ above, ...
2
votes
1answer
285 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
316 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 ...
7
votes
2answers
263 views

listplot very large numbers

Suppose we have the following function: NN = 150; W[n1_] := NN!/(n1 ! (NN - n1!)) (1/2)^n1 (1/2)^(NN - n1) Then we can Plot or Listplot it: ...
6
votes
1answer
173 views

Numerical error in Mathieu functions

Consider the MathieuCharacteristicA function, which is a piecewise function according to the documentation. The discontinuity happens at integer number. ...
5
votes
2answers
126 views

Display All Output Numbers in HEX

How might I modify Mathematica such that I can get the following functionality when working with HEX values. The odd lines are input and the even output. Red values should be the HEX values. ...
5
votes
2answers
915 views

Can the CholeskyDecomposition function in Mathematica be made to work on non-symmetric matrices?

The CholeskyDecomposition[m] function in Mathematica requires a symmetric and positive definite matrix m. For instance, the ...
4
votes
4answers
166 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: ...
4
votes
3answers
230 views

Increasing the precision of a calculation

Clearly I have misunderstood how to do this: I seem unable to understand how to get more digits out of a calculation and I can't see why - the following piece of code illustrates the issue. ...
4
votes
2answers
350 views

Quickly reducing the number of decimal digits for a set of real numbers

How can I quickly convert a number with $n$ decimal points to a number of with $m$ decimal points? Round works, however, it is slower than I would like. This ...
4
votes
2answers
531 views

Why doesn't FindRoot work correctly?

I'm trying to find the roots of the following equation: I need to find λs for different values of ξ. I know that for all ...
4
votes
1answer
168 views

Minimize failing on a polynomial

Calling: Minimize[{-0.4877 - 0.1190 r^2 - 0.1885 r^4 + 2.9703 z - 0.5531 z^2, 0 <= z <= 3.5 ∧ 0 <= r <= 1.75}, {r, z}] returns ...
3
votes
1answer
41 views

How shortening argument test when declaring functions?

When defining some functions which depend in many arguments sometimes we need to include question Q constraints to diminish processing time. My question is simple, there is a way to shorten a long ...
3
votes
1answer
472 views

Animated Wave Propagation using Fourier & InverseFourier

This is a continuation off of previous help on the first part of my project: fourier issue arising from input miscommunication Now I want to go one step further in the current code. Here's the code ...
3
votes
1answer
118 views

obtaining real roots of negative numbers in a long expression [duplicate]

I have a complicated symbolic expression which contains many terms like $(a/(a-2))^{1/m}$, where $a/(a-2)$ could be positive or negative after replacement. I only need the real root after ...
3
votes
2answers
467 views

Speed of convergence for NIntegrate

I'm trying to optimise numerically a function that entails computing the expected value of a truncated trivariate normal distribution and this is taking extremely long -I also get warned about ...
3
votes
1answer
1k views

Plot FindRoot for non-trivial function

I would like to plot the results of FindRoot over certain range of inputs. I tried to do this with the code: ...
3
votes
1answer
269 views

Strange behaviour of PolyLog Function

I discovered some strange behaviour of the PolyLog[] Function in Mathematica which seems to me like a bug in the function implementation. It looks like ...
2
votes
2answers
131 views

Steady State Numerical Solution of Heat Diffusion Equation in 2D

I'v been trying to solve for the steady state of the heat diffusion equation numerically but I cant seem to get it to work. My code is ...
2
votes
1answer
106 views

Breaking out of NDSolve

I am solving a coupled set of differential equations with NDSolve for 6 unknown functions of time. At a certain point in time, the system hits a singular point where the potential governing the ...
2
votes
1answer
181 views

Fourier Transform Help

I'm trying to do a Fourier Transform of the following Data, but I'm completely stuck. Here's what I've done so far: ...
2
votes
1answer
836 views

NDSolve runs out of memory

I need to solve a second order ODE numerically. The ODE depends on two parameters (a,b). Things work fine when 'a' is small, but for large 'a' the solutions are oscillating rapidly and Mathematica ...
2
votes
1answer
237 views

Numerical comparisons of matrices

I have a matrix which should be equal to a null matrix. However due to the numerical precision, a brutal equality test with a matrix initialized with zeros does not work. How should I perform the ...
1
vote
1answer
138 views

Why does it matter at what point I replace?

I need to find four orthogonal linear combinations of complicated functions, that vanish at four different points. I use (LK4 is defined below, but its shape should have nothing to do with my ...
1
vote
1answer
99 views

How to properly apply NumericQ or s.th. similar here? - NDSolve inside NMaximize

I wrote a function that numerically solves a given Schrodinger equation and returns replacement rules to obtain the time evolution operator. It looks and is used as follows: ...
1
vote
2answers
130 views

Increasing number of decimal places with FixedPoint

I've tried: In[169]:= newton3[x_] := N[1/2 (x + 3/x)]; FixedPointList[newton3, 1.0] Out[170]= {1., 2., 1.75, 1.73214, 1.73205, 1.73205, 1.73205} Of course: ...
1
vote
1answer
101 views

Applying N to the roots found by Solve gives complex numbers when the roots are real [closed]

I have a function which is f(x) = x^3 - 5 x^2 - x + 1. When I solve for x to find the zeros ...
1
vote
0answers
220 views

Problem with NDSolve in Mathematica 9 / 10

I'm having trouble by solving the following differential equation in Mathematica 9 and 10, where the code works fine in version 7: ...
1
vote
0answers
58 views

Rounding to the nearest decimal [duplicate]

If I have a bunch of numbers in a list {1.435243523432,2434.2321321412,5.8239897,...}, without multiplying everything by some power of ten and then dividing by that ...