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

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8
votes
1answer
209 views

SymplecticPartitionedRungeKutta shows strange error

Bug introduced in 9.0 or earlier and persisting through 10.2 or later I tried to solve Hamiltonian system ($Q$ is a vector of all generalized coordinates, $P$ - of generalized momentum) $$ \frac{\...
8
votes
1answer
227 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 ...
8
votes
1answer
709 views

Is there any automatic differentiation package?

I'm wondering if an automatic differentiation package exists for Mathematica. This is what I mean by automatic differentiation.
8
votes
1answer
132 views

FindMaximum failing on a trivial problem [closed]

I am trying to solve a trivial optimization problem with FindMaximum but for some reason it is not going. I reduced the problem down to the following non-working ...
8
votes
1answer
187 views

Exp of big negative numbers [duplicate]

I noticed that Exp have a strange behaviour with big negative numbers ...
7
votes
2answers
439 views

Position function not always returning an answer even with no apparent problems

I'm having some problems with Position. Sometimes it will give an empty list instead of the actual position of the element I am looking for when that element is ...
7
votes
1answer
236 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 ...
7
votes
2answers
180 views

Multiply integrand with -1, and the precision changes?

"After multiplying the integrand of NIntegrate with -1, the Precision of the output will ...
7
votes
1answer
1k views

How to solve fluid flow problem based on Navier-Stokes equations?

Does anyone know or can provide any examples how fluid flow problem can be formulated and solved in Wolfram Language? Simplest cases of 1D or 2D flows based on Navier-Stokes equations or even their ...
7
votes
1answer
278 views

Fractal dimension of a large networked molecular system

I am trying to determine the fractal dimension of this complex biomolecule (figure attached). Any clues as to how this can be done. In trying to determine this quantity, I wonder how its ...
7
votes
1answer
1k 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 ...
7
votes
2answers
201 views

Derivative of the Dedekind eta function fails to compute with errors I don't understand

When trying to understand better the question Eisenstein Series in Mathematica? I stumbled on the following: issuing Derivative[1][DedekindEta][.11 I] gives ...
7
votes
2answers
295 views

Mod[1.2, 0.2] is not equal to zero

Why doesn't the following expression evaluate to zero? In[1]:=Mod[1.2, 0.2] Out[1]=0.2 Edit: This is what I wanted to do: ...
7
votes
2answers
370 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: ...
7
votes
2answers
276 views

How to do multi-dimensional principal value integration?

The toy model is: $$\int_{-2}^{2}\int_{-2}^{2}\frac{1}{1-(x^2+y^2)}\, dx\, dy$$ The integrand have opposite sign across the circle $x^2+y^2=1$, so one would expect that the integral has meaning only ...
7
votes
1answer
873 views
7
votes
1answer
284 views

Synchrotron Radiation and ListDensityPlot

I'm trying to reproduce the following plots: As described by this blog entry: Synchrotron radiation As you can see in the linked article, the task is essentially to make a ...
7
votes
1answer
117 views

Need a generalization of RootApproximant to recognize linear combinations over algebraic numbers

RootApproximant does a very good job when I need to recognize an algebraic number and when enough of its digits are known (or even when an unlimited number of ...
7
votes
1answer
1k views

Using Mathematica to help to determine the consistency of and numerically solve systems of non-linear equations

The formal problem The question I am about to ask is applicable to many scientific and engineering problems. In short, I am bout to ask for pointers and practical advice for Mathematica beginners who ...
7
votes
1answer
147 views

Why don't 1. (0. + a) or (0. + 1. a) simplify?

I'm handling some mixed-numeric-analytic expressions, and I feel I'm missing some subtleties of how Mathematica handles simplification of such expressions. In particular, I was initially puzzled by ...
7
votes
0answers
278 views

Mathematica 7: “LessEqual::nord:” error when using NMinimize on a real function

Bug introduced in 7.0 or earlier and fixed in 9.0 I encounter a problem (Mathematica 7) similar to Strategies to avoid LessEqual::nord in NMinimize? but the advised strategies don't work for me. ...
6
votes
3answers
635 views

RK4 Gravity Simulator

I have the following RK4 solver which splits the two 2nd order ODEs, used to calculate x and y positions under the influence of a gravitating body where $$x''(t)=\frac{G m x(t)}{(x(t)^2+y(t)^2)^{3/2}}$...
6
votes
2answers
290 views

How to implement a numerically efficient Airy Zeta Function

Define the Airy zeta function for $n=2,3,\dots$, by $$ Z(n) := \sum_r \frac{1}{r^n}. $$ where the sum is over the zeros $r$ of the Airy function $\operatorname{Ai}$. In Mathematica the $\operatorname{...
6
votes
2answers
342 views

Inverse Laplace transform

Let $r=\mu = 0.15; \sigma = 0.05; T = 1; S_0 = 100; K = 95;$ Let $\nu:=\frac{2\mu}{\sigma^2}-1$ and $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
6
votes
2answers
509 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 ...
6
votes
3answers
369 views

Finding the square root of a squared number?

Taking the square root of the square of a number Variable set to a real value I'm wondering why these examples a = -4.3; Sqrt@a² Sqrt@(a^2) Sqrt[a^2] Sqrt[a²] ...
6
votes
2answers
372 views

Round vs. Floor vs. Ceiling for non-integers non-orders-of-magnitude

I understand that Round give the nearest even integer for cases where the number is between two integers, i.e. Round[2.5] = 2 ...
6
votes
3answers
639 views

Numerically integrating a list-valued function [duplicate]

I want to NIntegrate a List valued function foo[x] which is only defined for numerical ...
6
votes
2answers
564 views

Any ideas on how GeneralMiniMaxApproximation is implemented?

GeneralMiniMaxApproximation is used to construct minimax approximations of parametrically defined functions. I am curious about how ...
6
votes
2answers
151 views

How to speed up Min of DateObjects?

I'm in version 10.0.1 using a Dataset to do some plots and things. For one of the plots I need to get the minimum date of a some filtered set of the ...
6
votes
2answers
343 views

Infinite base two number to base ten

Suppose I have a base two number that repeats itself every five places (a number $x$ such that $0\le x<1$. For example: $$x=0.101011010110101101011010110101101011010110101...$$ What would be a ...
6
votes
2answers
225 views

Gamma function computation efficiency?

I wonder what kind of algorithm is used to compute the values for the gamma function. Specifically, I am interested in how the computational load increases when the complexity of the input grows. So, ...
6
votes
1answer
1k views

Mathematica NDSolve and 'Compile'?

Since the consensus is usually that NDSolve speeds fares badly against compiled code such as c++ ODE solvers using GSL say, is it possible to make up for this lag ...
6
votes
1answer
256 views
+50

How do I numerically evaluate and plot the Fabius function?

The Fabius function is a well-known example in analysis of a non-analytic function that is infinitely differentiable. I want to be able to numerically evaluate the function for any real argument, as ...
6
votes
1answer
590 views

Is there no documentation for Method in Eigensystem?

There does not appear to be any documentation on how to use Method in Eigensystem, or at least not in Version 9.0.1 of ...
6
votes
1answer
109 views

Why doesn't Rationalize work for 0. in Interval?

Same motivation as this q. Why doesn't Rationalize work for 0.? Interval[{0., 1.}] // Map[Rationalize, #, {2}] & ...
6
votes
1answer
223 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. ...
6
votes
1answer
262 views

Iteration process involving several functions

I would like to carry out a following iteration process: Apply function f1[a_,b_,c_,d_] to a starting list l1={a1,b1,c1,d1}, ...
6
votes
1answer
319 views

Numerical problems with calculation of function

I have a problem with a calculation which I try to do with Mathematica (8.0.1). I have the following function which describes a cone (with half opening angle theta)...
6
votes
1answer
209 views

Trouble with shooting method for a 4th-order differential equation

I'm trying to solve the following forth-order ODE with the shooting method: $$\frac{1}{5}(y-2xy^\prime)=\frac{1}{x}\left\{\frac{xy^\prime}{y}+xy^3 \left[\frac{(xy^\prime)^\prime}{x} \right]^\prime \...
6
votes
1answer
2k views

Mutual Information involving two matrix states

I basically retrieved the following technique of evaluating the mutual information involving two matrices from this site at http://bmia.bmt.tue.nl/People/BRomeny/Courses/8C080/default.htm The ...
6
votes
0answers
77 views

Negative accuracy numerics ( 0``-128 notation )

What does it mean to have a negative accuracy number? I understand 0``128 to mean "the number zero to 128 decimal points". Mathematica corroborates this: ...
5
votes
4answers
424 views

Display a number in Mathematica 9 in periodic form

I want to display a rational number in Mathematica in periodic style. PeriodicForm isn't working anymore. It worked in Mathematica 5 and now I'm using Mathematica 9....
5
votes
4answers
2k views

Numerical differentiation methods

Is it possible to write code in Mathematica that implements various differentiation methods (like forward, central, extrapolated, etc.)?
5
votes
4answers
3k views

Numerical Differentiation using 1500 data points

I have a set of 1500 data points (which are some energy eigenvalues) corresponding to a parameter H0 (which represents magnetic field. H0 values are equispaced going from $-3.0$ to $3.0$ in steps of $...
5
votes
2answers
262 views

Strange phenomenon occurring in analytic integration result involving Bessel functions

For the following integral, Integrate[x^2 Exp[-a x^2 - b x^4], {x, -∞, ∞}, Assumptions -> {a > 0, b > 0}] Mathematica gives the following analytic ...
5
votes
3answers
142 views

Differentiate a numerically defined function

My function is f[a_, b_] := NIntegrate[Sqrt[(Cos[t] - a)^2 + b^2], {t, 0, Pi}] I want to calculate g[1,1] where ...
5
votes
3answers
385 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) ...
5
votes
3answers
310 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. ...
5
votes
2answers
130 views

A problem with Compile and Map

There is a weird behavior of Compile that I do not understand. Consider the following example: ...