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

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4
votes
4answers
189 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
1answer
487 views

Using NDSolve to solve Equation of Motion in cylindrical coordinates

I have a set of coupled differential equations which represents the equation of motion of a particle in cylindrical coordinates with the following Hamiltonian: $$ H=\frac{1}{2m} \left( p_r^2 + ...
4
votes
2answers
188 views

Floating point addition not associative

Can anybody explain the following behavior? x = 0.2 + (0.3 + 0.1); y = (0.2 + 0.3) + 0.1; x == y (* -> True *) But actually the variables do not exactly ...
4
votes
1answer
248 views

Numerical errors/inaccuracies in ProductLog

Context In cosmology, a fairly accurate model to describe the gravitational potential, $\psi(r)$ of dark matter halos is given by $\psi( r)=\log(1+r)/r$. ...
4
votes
1answer
107 views

Strange behavior of Mathematica regarding calculation time

Today I witnessed the following strange behavior of Mathematica, when it comes to calculation time involving larger nested lists. The following is the short example that I setup, I am sure one can ...
4
votes
1answer
413 views
4
votes
1answer
431 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 ...
4
votes
1answer
926 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 ...
4
votes
1answer
100 views

Why doesn't NSolve work for this equality? Wildly incorrect solutions are given in certain cases

I am trying to write a function that solves for p in the following equation: PDF[BinomialDistribution[n, p], x] == op The ...
4
votes
2answers
195 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. ...
4
votes
1answer
177 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 ...
4
votes
1answer
97 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 ...
4
votes
1answer
181 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: ...
4
votes
1answer
227 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
2answers
383 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
1answer
117 views

NExpectation not up to expectations with Boole or Conditioned

Context I am interested in computing numerically the number of extrema at a given threshold for random fields. These numbers are expectations of MultinormalDistributions. Problem This integral ...
4
votes
1answer
316 views

How to fix errors in Gram-Schmidt process when using random vectors?

I first make a function to get a random vector on unit sphere in a swath around the equator. That is what the parameter $\gamma$ controls; if $\gamma = 1/2$, the vectors can be chosen anywhere on the ...
4
votes
2answers
71 views

Is there a way for accuracy backtick notation to accept variable inputs?

Backtick notation uses 1.0``20 to give 1 with 20 places of accuracy after the decimal point. But what I want is ...
4
votes
2answers
116 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: ...
4
votes
0answers
99 views

Synchrotron Radiation and ListDensityPlot

I'm trying to reproduce this plots: For this task i'm following this blog entry: Synchrotron radiation As you can see there, the task is to make a DensityPlot of a vector field essentially. This ...
4
votes
0answers
1k views

Numerically solving system of partial differential equation

I am trying to solve a system of partial differential equation with boundary conditions. But I got an error message saying NDSolve::icfail: Unable to find initial ...
3
votes
2answers
291 views
3
votes
2answers
611 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 ...
3
votes
2answers
261 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 ...
3
votes
3answers
826 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 ...
3
votes
1answer
416 views

N[number, 100] does not give 100 decimal places [duplicate]

Please look at this computations: a = N[Sqrt[2], 20]; N[a^2, 100] The output is 2.0000000000000000000, which is apparently not $a^2$ to 100 decimal places. ...
3
votes
2answers
261 views

Computing the minimum distance in a contour plot

I have the following Mathematica code ...
3
votes
2answers
209 views

Storing Variables in “Loops” and Point Plotting

Given the function $y=\sin x$ defined over the region $-\pi \leq x \leq \pi$, I need to implement a "do loop" such that I sweep over 100 or so points $-1 \leq y \leq 1$ and find precisely the two $x$ ...
3
votes
3answers
287 views

How can I find the sum of the even digits of a number of all elements of a list?

Let $E(n)$ denote the sum of the even digits of $n$. For example, $E(123456789) = 2 + 4 + 6 + 8$. I tried a = IntegerDigits[123456789] and ...
3
votes
3answers
150 views

Solving determinant of a Kronecker product of matrices gives a numerical error - why?

I am doing the following steps (code at the end of the post): I start with a 2x2 matrix (smatrix), which is a function of a single variable (u2). I want to set the determinant of this matrix ...
3
votes
2answers
515 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
206 views

Why to do parentheses change the results of a calculation?

I'm getting results that are sensitive to where I place parentheses with respect to operations that are associative1 (and should thus be insensitive to such placement). For example, if I define2 ...
3
votes
2answers
74 views

Maximizing a function defined using NIntegrate [duplicate]

I have two functions fn[x,y,z] which is in integral form and I have another function gn[x,y] which is also in integral form ...
3
votes
1answer
91 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 ...
3
votes
2answers
338 views

NMinimize/NMaximize is unable to generate initial points

Mathematica 10 generates a warning that it is unable to generate initial points for numerical optimization problems. I picked a particularly simple example. The problem goes away when ...
3
votes
2answers
184 views

Rounding the coeffcients in a polynomial

I have a very large polynomial with Complex Numbers as coefficients. Due to many calculations, there are rounding off errors. I know however by theoretical considerations, that the coefficients are ...
3
votes
1answer
120 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
1answer
120 views

compute the gradient in high dimension

The following code is used to compute the gradient of a given 2D data. ...
3
votes
1answer
211 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
489 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
3answers
1k views

Implementing Newton's method

I have this question on coding Newton's method in Mathematica. I have some code to go by but I have no clue if it's computing the functions in the right order. The book is the numerical methods ...
3
votes
2answers
65 views

How to use Evaluation Monitor in conjunction with NonlineaModelFit?

I am trying to find out how many function, gradient and hessian evaluations are made when i run NonlinearModelFit for example in this case ...
3
votes
2answers
116 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): ...
3
votes
2answers
121 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 ...
3
votes
1answer
216 views

Find the NullSpace of a matrix whose determinant is “almost” zero

If $A$ is a matrix such that $\det(A)=0$, it is easy to get a basis of the kernel of $A$ with NullSpace[A]. Now let's consider a matrix $B$, function of a ...
3
votes
1answer
126 views

Bad numerical approximations

I'm trying to do some calculations here, but for some reason Mathematica starts using numerical approximations that are no good for my work. Specifically: ...
3
votes
2answers
181 views

Solve-ing with initially unassigned parameters and Solve-ing using their numerical values produces different results

I am trying to solve an equation using the following piece of code: ...
3
votes
1answer
861 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 ...
3
votes
1answer
278 views

Numerical Error with Large Matrices

I am writing a Finite Element Analysis program in Mathematica. The code involves handling a large matrix with large entries. I get an error when I try to use Mathematica's "LinearSolve" to solve a ...
3
votes
1answer
279 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 ...