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

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10
votes
2answers
747 views

Why is Mathematica destroying this graph?

Here I have a picture of a function I graphed: reg[x_,y_]:=(x^2+y^2)Cos[4ArcTan[y/x]]; Plot3D[reg[x,y],{x,-2,2},{y,-2,2},AxesLabel->Automatic] And here is ...
0
votes
1answer
47 views

Find numerical solution to this system of DE

I am trying to solve this system $$\left( \begin{array}{ccccc} 2 k & -k & 0 & 0 & 0 \\ -k & 2 k & -k & 0 & 0 \\ 0 & -k & 2 k & -k & 0 \\ 0 & 0 &...
1
vote
0answers
47 views

High Precision Plots of Eisenstein Series [closed]

When plotting the Eisenstein Series (great information here Eisenstein Series in Mathematica?) you observe highly non-trivial branch cut behavior close to the real axis. This makes the numerics break ...
2
votes
2answers
57 views

How do I overcome an Overflow?

I'm trying to calculate entropies for an absolutely giant system by counting states, and this means I have to use some obscenely large numbers. I'm running ...
0
votes
1answer
59 views

Unexpected result: Numerical and analytical results do not match! [closed]

I am calculating the eigenvalues and eigenvectors of a matrix. This is my code: ...
0
votes
0answers
37 views

Is it possible to get the error estimates of predicted values computed by FindMinimum using the Levenberg Marquardt method?

I use the LevenbergMarquardt method of the FindMinimum function to minimize a residual function (mathematical-optimization). This residual function is computed from experimental data and the solution ...
1
vote
1answer
146 views

NDSolve with coupled ODE's and unknown singularities

I have two coupled ODEs that I am trying to solve numerically. It appears that there is a singularity in the solution to the equations which I am unsure how to get past. Both functions $\alpha$ and $\...
3
votes
0answers
89 views

Computation of a Fresnel Diffraction pattern with Discrete Hankel Transform

In the next link: Computation of Hankel Transform using FFT (Fourier) Rainer implemented a great solution given in the next reference: Manuel Guizar-Sicairos and Julio C. Gutiérrez-Vega, "Computation ...
3
votes
2answers
52 views

Numerically solving coupled ODE's with a parameter as initial condition

i'm currently trying to numerically solve a set of coupled ODE's to obtain the functions p(r), h(r) and m(r) in the range of r1 <= r <= r2 with initial conditions m(r1)=a=const and p(r1)=b=const....
0
votes
0answers
52 views

Eigenelements of conductivity equation

I am trying to calculate the eigenvalues and eigenfunctions of the conductivity equation in an annulus. In particular I am looking for $(\lambda, u)$ s.t. $$ \begin{cases} \Delta u = \lambda u & \...
2
votes
0answers
61 views

Why can Mathematica compute numerical sums more efficiently when they are written as matrix operations?

Let $f(n)$ and $K(n,m)$ be functions such that the double sum, which we wish to evaluate numerically, $$ \sum_{n=1}^a \sum_{m=1}^a f(n) f(m) K(n,m) $$ exists when $a$ is some large positive number. I ...
1
vote
2answers
117 views

Numerical integration does excessive coarse-graining?

I am trying to perform numerically the following integral $$\int_0^8\text{d}x\,\text{Re}\left[\frac{e^{-\frac{a^2}{2}-\frac{x^2}{2}} x^4 \sin (b x)\left(e^{-i c x} \text{erfc}\left(\frac{-c +i x }{\...
3
votes
0answers
80 views

Kernel crashes when computing finite difference mixed derivative with respect to y & z but works fine when computing with respect to x & y or x & z?

I am using Mathematica 10.4.0 on Ubuntu 16.04. I am trying to solve a set of differential equations using finite difference method on an NxNxN cubic grid (x, y, z directions). I am getting a weird ...
5
votes
1answer
75 views

Finding the correct boundary conditions to a specific problem

I want to reproduce the following problem in the figure: $$\phi''+c\phi'\sqrt{m^2\phi^2+\phi'^2}+m^2\phi=0$$ where $\phi=\phi(x)$ with $x \in (-\infty,\infty)$, $c=\sqrt{3/2} \ $ and $m=0.2$. ...
1
vote
2answers
97 views

NSolve won't act on very large powers

I noticed that NSolve isn't running properly when I have some seemingly harmless numbers in my expression. Here is a simple example: ...
5
votes
1answer
76 views

ComplexInfinity for a convergent product

The infinite product involving the ratio of (n^2)! to its Stirling approximation ...
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 ...
0
votes
1answer
97 views

Using Neumann boundary conditions

I had a semi-related physics problem I needed to solve analytically (which I have already done), but I am now curious how I would go about numerically solving the entire system in Mathematica. ...
18
votes
1answer
507 views

Numerical inverse Laplace-Hankel transform

When trying to reproduce the result of this paper about numerical solution of Lamb's problem, I encountered the following double integral (to be more precise, the 0-order inverse Hankel-Laplace ...
0
votes
2answers
104 views

Numerical derivative from data points

I want to take the second derivative of a set of data points (at the point $x = 0$). Let's assume that this set looks like that ...
2
votes
1answer
75 views

Accuracy limitations of singular value decomposition?

in the process of working on a physics problem I have found the need to use the singular value decomposition function built into Mathematica. I have encountered what seem to be limitations to the ...
2
votes
1answer
122 views

Mathematica Precisions vs Doubles in C/C++

I'm having a bit of an issue regarding numerical precision and I'm not sure how to deal with it. I have a certain randomly generated matrix, say $M$, that I wish to compute the eigenvalues. The ...
0
votes
0answers
46 views

Problems with numerical solution of differential equation

I'm trying to obtain a numerical solution for my differential equation. But i have the following mistake: Encountered non-numerical value for a derivative at z == 0. Can somebody help with that? <...
2
votes
3answers
97 views

FindMinimum step size too small

I'm running a simulation of an electromagnetic system using Radia, an external code that is run from Mathematica. I want to use FindMinimum to determine some ...
14
votes
2answers
324 views

What can one do with extremely stiff problem in NDSolve?

Consider the following illustrative problem: $$ \frac {\partial f} {\partial t} = \frac {\partial} {\partial x}(x f) + \frac {\partial} {\partial x}(f \frac {\partial f} {\partial x}) $$ This is ...
4
votes
1answer
354 views

How to calculate accurate answer in Mathematica?

I accidentally discovered for myself, that Mathematica outputs inaccurate answer. For instance, if I take $\sin(2 \cdot \pi \cdot 0.5) = 0 $, then in Mathematica it is: But if I calculate it on ...
1
vote
1answer
61 views

Precision in calculation [duplicate]

I am writing some code to demonstrate the effect of the number of significant figures a coefficient has on the solution of a nonlinear equation. I define the coefficient as follows: ...
0
votes
0answers
43 views

Difficulty in replacing variables with list of variables for a function for FindMaximum application

FindMaximum gives incorrect answer when I redefine a function by changing its arguments from variables to a list of variables. The code goes as follows ...
0
votes
1answer
130 views

How can I solve a Hamiltonian with numerical methods?

Hamiltonian in terms of two level atom's operator (0 is ground state and 1 is excited state) which are 2*2 matrices and cavity modes are given by $a$ and $a^\dagger$. Rest of the parameters are ...
0
votes
1answer
58 views

Transform a variable's exponent from an exact rational to an inexact decimal

here is a little problem I could not find a solution for. I have a variable with an exponent represented as a fraction, for example, var = a^(39/106) Now I ...
0
votes
0answers
65 views

Another question about inverse Laplace transform

Given $r = 0.06;\quad \theta = 105;\quad \kappa = 1;\quad x_0 = 100;\quad K = 100;\quad \sigma = 0.10;\quad T = 0.25;$ Define $ \nu = -\kappa/\sigma^2 - 0.5;\quad p = \kappa*\theta/\sigma;\quad q = -\...
0
votes
0answers
55 views

Solving a Volterra type (second) integral

I am trying to numerically solve this Volterra type integral equation. The equation I'm plugging in is a simplified version of We will take $H(\eta')$ and $q(\eta)$ to be 1 for now. $\mu$ is = $\...
2
votes
2answers
101 views

How to find the integrand singularity points when having NIntegrate::slwcon:

In order to calculate the closed area of the curve below defined by parametric equation curve02, ...
3
votes
1answer
50 views

My NIntegrate expression returns a wildly inaccurate value

I am trying to integrate a function using NIntegrate: ...
12
votes
1answer
140 views

A weird issue with Interval[$MaxNumber]

From the Interval documentation: For approximate machine- or arbitrary-precision numbers x, Interval[x] yields an interval reflecting the uncertainty in x. <...
-1
votes
2answers
121 views

Numerical approximation using trapezoidal formula [closed]

I have bumped into a problem, that I cannot solve. I have to approximate the value of ln3 using a composite trapezoidal formula, so that the error should be within (10)^-3! How can it be solved?
9
votes
4answers
282 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 ...
1
vote
0answers
107 views

How to find the eigenvalues of a custom operator using NDEigensystem? [closed]

I would like to solve a Hamiltonian presented by a 2x2 matrix. Hamiltonian is given by: ...
4
votes
0answers
69 views

strange FullSimplify result, why zero? [duplicate]

This came up looking at this How to speed up calculation of this equation (FindRoot). Is there some sense to why FullSimplify gives zero here? ...
3
votes
1answer
161 views

Errors Solving Elliptic PDES with FEM

I am trying to solve the equation below governing transversely isotropic plane strain in cartesian coordinates with the given boundary conditions based on code found here using Mathematica 10.1 on OSX ...
0
votes
1answer
138 views

Solving a nonlinear systems of coupled differential equations with boundary conditions

I am trying to solve the following systems of coupled differential equations with boundary conditions (BC) at $0$ and at $∞$ : $y_{1}'(x)=\frac{-\sqrt{\frac{2}{\pi}}\,\frac{\alpha}{18}\,x^4+x\,y_{2}(...
5
votes
2answers
152 views

Evaluate numerically an extremely small number

How to evaluate numerically $e^{-4 \cdotp 10^{35}}$ in the form $0,a_1a_2...\times 10^{-n}$ ...
10
votes
2answers
275 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 ...
1
vote
0answers
40 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
0answers
45 views

EvaluationMonitor and variables with indices + subscripts

I have encountered the following problem while using EvaluationMonitor with NMinimize: variables that have both a subscript and an index, e.g. Subscript[x,y][1] do ...
3
votes
2answers
166 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 ...
0
votes
1answer
64 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
75 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]: <...
3
votes
1answer
75 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
258 views

Rotating an Interpolating Function

I have used the following code to generate eigenfunctions of a PDE: ...