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

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16
votes
4answers
616 views

How to remove duplicates from set of machine precision 2D points?

I have a set of 2D points with machine precision coordinates. I need to remove all duplicates. Performance is important. This is the most obvious fast solution: ...
3
votes
1answer
203 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 ...
23
votes
2answers
534 views

Symbolic derivatives are being calculated numerically

Just found the following while debugging a problem. Mathematica is calculating the derivative of IntegerPart[x] in some odd way: ...
10
votes
2answers
258 views

What is the fastest way to compute digits of $\pi$ using Mathematica?

There are a lot of ways to calculate digits of $\pi$ using Mathematica. The most naïve way I can think of is N[π, 100000000] Of course, there are a lot of fast ...
5
votes
2answers
147 views

Evaluate numerically an extremely small number

How to evaluate numerically $e^{-4 \cdotp 10^{35}}$ in the form $0,a_1a_2...\times 10^{-n}$ ...
1
vote
1answer
72 views

Paramter Scans and $\chi^2$ Test in Mathematica

Is there any in-built function or a recommended package that enables one to find, say, 10 Parameters, which are used as boundary conditions in NDSolve, that minimize $\chi^2$? ...
0
votes
1answer
51 views

LinearSolve on non-square matrices?

I just came across a strange behaviour for LinearSolve (on Mathematica 8.0.0.0). Consider the following definitions: ...
0
votes
1answer
71 views

Integrate over FindRoot solutions

I have a function of bivariate normal PDF and its marginals defined as ...
1
vote
0answers
39 views

solving with numerical methods [closed]

Hi I would like to solve the equation below in Mathematica.Since I am a beginner I can not solve it with NSolve and Solve.I don't know why.Do you have any idea?! ...
0
votes
1answer
103 views

Precision of Eigensystem? [closed]

I was using Eigensystem to obtain the rotation matrix. However, I find out Mathematica does not fully diagonalize my matrix (or say not precise enough). My matrix ...
12
votes
7answers
681 views

Numerical evaluation of a sum

I am trying to compute numerically NSum[(-1)^n/n^3, {n, 1, Infinity}]. Of course, using first Sum would work here, but often ...
3
votes
2answers
150 views

Plotting Planck's function and unexpected results

I have the code below. If you look at the plot, you can see a strange behaviour. The function goes to zero as λ->0 but you can see the plateau below ...
34
votes
0answers
1k views

Fast Spherical Harmonics radiative transfer

This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me. I am using ...
2
votes
0answers
73 views

Number recognition in Mathematica [duplicate]

Suppose that I have a number $n$ with many decimal digits of precision. What is the code to use to get Mathematica to recognize possible closed-form expressions for that number?
0
votes
1answer
58 views

Can't sort my list numerically for larger numbers than 10 e.g. 1,10,100,2 [duplicate]

I want my files names in real numerical order so 1,2,3,10,12. However it is currently putting them in order like so: 1,10,12,2,3 Input: ...
3
votes
0answers
73 views

Low accuracy while solving a multi-variable equation numerically

My question is as following: I was trying to make a function Vs2[r] with two parameters fit a set of conditions. Vs2[r]: ...
1
vote
1answer
73 views

Estimating error in NDSolve

I would like to give a theoretical estimation of local truncation error (and then for the global one) for a solution to a numerical initial value problem by ...
3
votes
1answer
68 views

Split Boundary Value Problems win Algebraic Equations

Is it possible at all to solve with NDSolve (or other built in function) a split boundary value problem with algebraic equations? Please look at the following example: ...
4
votes
2answers
253 views

Rotating an Interpolating Function

I have used the following code to generate eigenfunctions of a PDE: ...
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) - ...
14
votes
1answer
282 views

Non Standard Eigenfunction Plots of the Laplacian Over the Unit Square

I have recently been plotting eigenfunctions of the laplacian over the unit square using the NDEigensystem command. However, I have noticed something in the plots ...
2
votes
1answer
113 views

Basic 2D convolution with mathematica

Can anyone tell me why the following keeps burning my CPU without ever producing the desired plot? ...
3
votes
0answers
92 views
24
votes
3answers
828 views

Exponential fitting - isn't actually a BUG there?

There are many questions on this site about wrong exponential fitting in Mathematica but no one considers this well-known problem as a potential bug. Usually people suggest well-known workarounds ...
1
vote
0answers
100 views

Numerically Solving Helmholtz over the Rectangle - Why does this code only give eigenfunctions of the form $u_{m1}$ [closed]

I have been following the method for numerically solving the Helmholtz equation in this example (the answer by User21) and have come across two problems. I have been implementing the method for a 2x1 ...
3
votes
3answers
151 views

Smooth initial data

I need something that produce pseudorandom smooth initial data for modelling phase separation equations (Cahn-Hilliard and simular). Generator code for now: ...
4
votes
1answer
59 views

Computing the logarithmic spectral norm rapidly

I wish to compute the logarithmic spectral norm of a square matrix $A$, which is defined by \begin{equation} \mu_2[A]=\lim_{t\downarrow0}\frac{\|I+tA\|_2-1}{t}. \end{equation} Hence, I simply code ...
0
votes
0answers
30 views

How do I numerically integrate the result of NDSolve if it depends on several variables?

I am trying to numerically integrate solution of NDSolve. I am trying to integrate my result of NDsolve in line 97 of my notebook, but am getting the error ...
0
votes
0answers
75 views
0
votes
1answer
93 views
5
votes
1answer
218 views

Trouble with shooting method for a 4th-order stiff ODE

The ODE I need to solve is $$\left(y^3y^{\prime\prime\prime}\right)^\prime+\frac{5}{8}xy^\prime-\frac{1}{2}y+\frac{c}{y}=0$$ where $\prime$ denotes differentiation, $c$ is a constant and ...
1
vote
1answer
43 views

Differential equation for a list with parameter dependent function

I am having a differential equation: y' = (1 - y) - f[y, mu] y; f is a hysteretic function that depends on y and on the derivative of y: ...
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 ...
3
votes
0answers
96 views

Constructing the coefficient matrix in discretization of a PDE

In order to solve the following two dimensional PDE $$\frac{\partial u(x,y,t)}{\partial t}-\frac{1}{2} \sigma _1^2 x^2 \frac{\partial ^2u(x,y,t)}{\partial x\, \partial x}-\frac{1}{2} \sigma _2^2 y^2 ...
2
votes
1answer
200 views

Maximized value of a function as an additional constraint on a variable

I want to maximize a function $f(b, h)$ with respect to its arguments and subject to some additional constraints. If these constraints are satisfied, $f$ is increasing in $h$. I then want to find an ...
3
votes
1answer
385 views

Wrong result of simple math calculation. Is it possibly a bug of the program? [closed]

I encounter the following issue accidentally (shown in the screenshot) which is very odd to me. The output[4] and [5] is obviously wrong. But with the input value of 991.91, it turns out to be right ...
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 ...
6
votes
1answer
195 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 ...
5
votes
0answers
70 views

How does Plus work on machine precision Real arguments?

I thought Kahan's summation method would make a nice example for students to use to think about round-off error [W. Kahan, Pracniques: Further Remarks on Reducing Truncation Errors, Commun. ACM 8  ...
1
vote
1answer
95 views

How can I increase the precision of my computation?

How can I increase precision up to 15 digits for the results (EC, and that of FindRoot) computed below? ...
3
votes
2answers
104 views

Unexpected behavior from Accuracy

This is my code Table[With[{x = 10^n + 1/17}, N[x, {Infinity, 5}]], {n, 0, 5}] // Column Or like this ...
1
vote
1answer
103 views

Wrong root when using numerical values

I have the following inequality: $$ \sqrt{\frac{a}{2x}}+ \frac{b}{1-\frac{a}{a+\sqrt{a(2bx + a)}}} + \frac{a}{2x\frac{a}{a+\sqrt{a(2bx + a)}}\left(1-\frac{a}{a+\sqrt{a(2bx + a)}}\right)} < f $$ on ...
1
vote
1answer
45 views

System of ODEs - NDSolve issues

I am a self-taught beginner trying to use Mathematica for the first time. If you wouldn't mind, I would like to ask for help with the code I am working on as I keep running into multiple issues when ...
5
votes
1answer
102 views

Compilation, square roots, and integers

After looking at this question, particularly this answer, I wrote my own performance test, using the two functions ...
4
votes
1answer
130 views

Saved InterpolatingFunction behaving badly

Bug introduced in 10 and persists through 10.3.1 or later I created this InterpolatingFunction, and NIntegrate gives an ...
0
votes
2answers
58 views

How to plot the solution of a function while varying a parameter [closed]

I have a function of a single variable that I want to solve numerically for different values of a parameter and then plot the results. I have a general equilibrium model that I can get to a reduced ...
0
votes
0answers
57 views

Error message when using a compiled function in NSum [duplicate]

Below is a simple example to illustrate the problem test = Compile[{{n, _Integer}}, n] Now, Table works fine ...
3
votes
3answers
70 views

EvenQ not working properly on IntegerPart[real number]

Something fascinating is happening at the moment. ...
7
votes
1answer
266 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 ...
1
vote
1answer
324 views

How can I use Mathematica to solve a Stefan Problem using an explicit scheme?

I would like to plot the temperature distribution for a particular case. the problem is stated in the paper, behind a paywall here, summarized as Consider a one-dimensional container of length l, ...