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

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13
votes
1answer
2k views

Kramers-Kronig in Mathematica

I am trying to calculate the change of the refractive index from the change of the absorption coefficient using the Kramers-Kronig relations, in Mathematica. ...
9
votes
3answers
276 views

Labeling solutions of an Eigenvalue equation involving Bessel functions

I'm solving the Schrödinger equation for a particle in an annular geometry with hard wall boundary conditions and I've reduced it to the following equation: $$J_m(k\,R_1)\,Y_m(k\,R_2) - ...
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 ...
3
votes
2answers
149 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
324 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
483 views

What is the correct way to use NIntegrate inside the FindMinimum function?

I'm having minor issues with the FindMinimum function when using NIntegrate inside. The functions work perfectly well but I get ...
39
votes
1answer
1k views

How to compare power towers in Mathematica?

First I tried it directly, but it overflowed: ...
14
votes
2answers
3k views

How to discretize a nonlinear PDE fast?

I wish to numerically solve the following PDE. Although there are some complete discussions for solving PDEs in tutorial/NDSolvePDE, there is no hint for the nonlinear case by discretization. Thus, I ...
20
votes
5answers
5k views

How can I differentiate numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
20
votes
2answers
776 views

Obtain approximate Hessian using FindMinimum

According to the documentation, when FindMinimum is told to use the method "QuasiNewton" on a unconstrained problem, it uses the ...
19
votes
1answer
426 views

Faster binary Hamming weight for big integers?

While working on an answer to Count the sequences in an array I found that DigitCount was the bottleneck in my code when used as ...
12
votes
1answer
2k 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
612 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 ...
15
votes
1answer
475 views

Why is MainEvaluate being used when LinearSolve can be compiled?

According to this question LinearSolve can be compiled. However, CompilePrint[] shows a call to ...
7
votes
3answers
3k 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
2answers
332 views

How to make the computer consider two numbers equal up to a certain precision

My problem is that I have a matrix A and the computer says is not Hermitian (self-adjoint). Then I check which elements make A ...
14
votes
3answers
392 views

Make mathematica treat $e_i^2$ as numeric

With NumericQ[symbol] = True, I can declare that a symbol is numeric. I want the expressions matching: $$e_{\text{i$\_$}?\text{IntegerQ}}^2$$ to be treated as ...
17
votes
0answers
231 views

Is MathieuC for moderately large imaginary arguments broken?

I'm trying to plot MathieuC[-3,0.3,I x] for $x\in[0,10]$, and here's what I get even with arbitrary precision arithmetic (here I use ...
4
votes
2answers
293 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. ...
3
votes
2answers
705 views

Unexpected result of summation

I wrote a small module that gives me an incorrect output-set. It should be a single number! I don't understand what went wrong. This is the form of summation used: $$\frac{1}{2} (b-a) \sum_{i=1}^n ...
12
votes
4answers
642 views

Why is Poisson Random Deviate Generation so slow?

I am generating Poisson deviates for some numerical work. Mathematica 9.0.1 is very slow in generating these random numbers, as can be seen below. ...
3
votes
3answers
128 views

Chopping matrix elements, real or imaginary

An undesired shape of a matrix has the following form: which is created by ...
2
votes
1answer
1k views

why there is a small imaginary part [closed]

I encountered a problem. I have a eigenvector eigvsI[1] ...
36
votes
3answers
6k views

Understanding differences between Maple and Mathematica in examples picked by Maplesoft

I am reading the document How Maple Compares to Mathematica. On page 15 there is an example where Mathematica produces wrong results. Does anybody know why? MAPLE: MATHEMATICA: Also on page 17 ...
25
votes
4answers
2k views

How to use NDSolve to track equilibrium?

I am looking for an extension of NDSolve where integration runs until certain variables are settled at an equilibrium. Now I have a working solution in my sleeves ...
21
votes
3answers
451 views

How to improve performance of BesselJ to the level of GSL?

Consider the following code: zs = N /@ Range[0, 12, 10^-5]; AbsoluteTiming[bessels = BesselJ[1, #] & /@ zs;] Length @ zs I've tried to measure only ...
12
votes
1answer
285 views

Eisenstein Series in Mathematica?

Mathematica doesn't seem to have built-in tools to deal with the Eisenstein series: $$\begin{align*} E_{2}(\tau)&= 1-24 \sum_{n=1}^{\infty} \frac{n e^{2 \pi i n \tau}}{1-e^{2 \pi i n \tau}}\\ ...
7
votes
2answers
680 views

How to apply restrictions to the “integrated” variable, when using NDSolve?

I have to integrate an energy along a path. I know the energy at the "beginning" of the path (energy[0]), and I can determine the energy change (gain and loss) ...
7
votes
3answers
405 views
20
votes
1answer
686 views

How to determine BLAS/LAPACK implementation used internally for numerical matrix operations?

Is there a command which reveals which implementation of BLAS and LAPACK are used in Mathematica's matrix operations such as Eigensystem? I asked a related question ...
14
votes
3answers
1k 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 ...
3
votes
1answer
131 views

Derivation of numerical scheme for linear transport equation on a variable stencil

The question is about automatica derivation of coefficients of numerical scheme on a variable stencil. So, lets consider 1d transport equation \begin{equation} (1)\qquad u_t+u_x=0. \end{equation} To ...
2
votes
1answer
4k 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
1answer
2k 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 $$ r\frac{d}{dr}\left(\frac{1}{r}\frac{d}{dr}A(r)\right)-\xi^2F(r)^2\left(A(r)-1\right)=0 $$ $$ ...
11
votes
1answer
349 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: ...
10
votes
5answers
330 views

Function for a series of joined slopes

I need a function for a series of joined slopes and my solution feels a bit kludgy. Is there a better way? A list of pairs of transition points and slopes: ...
10
votes
1answer
704 views

ParallelEvaluate for function minimization

Is there a parallelized version of a minimization routine available in Mathematica? The objective function is non-linear and the gradients have to be numerically computed. Every function evaluation ...
8
votes
1answer
1k views

Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
4
votes
3answers
181 views

How to read the intersect corodinate of two lines from the ListLinePlot?

Suppose I have two curves intersect at some point, how can I read the coordinates from the graph, not read by eye, but find it with more precision by computer. For example, here are two lists created ...
14
votes
2answers
452 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
2answers
738 views

Finding differences between Pi with varying number of decimals

I have the following code In[32]:= N[Pi, 2] Out[32]= 3.1 In[33]:= N[Pi, 1] Out[33]= 3. In[34]:= N[Pi, 2] - N[Pi, 1] Out[34]= 0.*10^-1 Why can't Mathematica ...
7
votes
1answer
145 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 ...
5
votes
0answers
656 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?
4
votes
1answer
531 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 ...
3
votes
1answer
312 views

Fixed-Point Numbers in Mathematica

I am working with a library that needs input in a Fixed Point notation. I’d like to figure out a way to convert the floating point results into fixed point representation. The fixed point length is ...
3
votes
1answer
2k 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
1answer
325 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 ...
10
votes
3answers
383 views

Bug: Wrong results from NSolve on coupled polynomials. WorkingPrecision->Automatic fails

OP UPDATE: I received an email from WR on 1-18-2016: "...It does appear that the NSolve function is not behaving properly in this case and I have forwarded an incident report to our developers with ...
9
votes
4answers
248 views

How to find the next root larger than a specified value, numerically?

I would want to have a general-purpose, reasonably robust method of finding the next numerical root above a specific value of x. I'm stumped by the fact ...
8
votes
1answer
204 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) $$ ...