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

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3
votes
0answers
101 views

Classification problem using SVM methods

I am running SVM on mathematica and I a used this code with classes: ...
2
votes
1answer
136 views

Basic 2D convolution with mathematica

Can anyone tell me why the following keeps burning my CPU without ever producing the desired plot? ...
24
votes
3answers
839 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
113 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
161 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
62 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
35 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
1answer
96 views

How to fit parameters, not functions?

Given a set of parameters ...
0
votes
0answers
86 views

Solving numerically a system of equations using different methods

I will use, as an example, the simple Henon-Heiles potential ...
1
vote
1answer
76 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 $\chi^2$? ...
1
vote
1answer
45 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: ...
0
votes
1answer
71 views

Integrate over FindRoot solutions

I have a function of bivariate normal PDF and its marginals defined as ...
5
votes
1answer
281 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 $0<c\le1$....
0
votes
1answer
69 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: ...
2
votes
1answer
205 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
396 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 (...
5
votes
0answers
72 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
116 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
141 views

Chopping matrix elements, real or imaginary

An undesired shape of a matrix has the following form: which is created by ...
6
votes
1answer
208 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 \...
9
votes
3answers
299 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) - J_m(k\,R_2)\,...
3
votes
2answers
105 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
49 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
107 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
131 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 ...
10
votes
3answers
400 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 ...
0
votes
0answers
58 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
71 views

EvenQ not working properly on IntegerPart[real number]

Something fascinating is happening at the moment. ...
1
vote
1answer
90 views

singularity in boundary value problem

I am trying to solve a non linear differential equation with variable parameter. ...
13
votes
2answers
608 views

more numerically accurate inverse matrix

I encountered the following matrix mat = {{2, 2.161209223472559` + 1.682941969615793` I}, {2.161209223472559` - 1.682941969615793` I, 2}} and ...
1
vote
0answers
45 views

Rescale large numerical factors in rational functions

Given a rational function $$ f(x_1,x_2) = \dfrac{r_1 x_1^2 + r_2 x_2}{r_3 x_1 + r_4 x_2}, $$ with $r_i$ arbitrary real or complex numbers, is there a built-in function to get Mathemtica to rewrite as $...
3
votes
2answers
72 views

Solving an integral equation for upper boundary

I am reading a paper on High Harmonics Generation (HHG) and a Lewenstein model The paper is here. I would like to reproduce some results but I am stuck at the following problem. I have: $$p(\tau_b,\...
6
votes
2answers
341 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 $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
10
votes
2answers
225 views

Demonstrating the behavior of a function as its independent variable approaches zero

I have several questions regarding the function $$f(x)=\frac{\sqrt{x^2+9}-3}{x^2}$$ that I would like to help my students with in the upcoming semester. Now, the limit as $x\to 0$ is 1/6. ...
3
votes
1answer
38 views

How can I perform arithmetic on a list integers and some other exact numbers and get decimal numbers in the result?

I want to do a simple calculation with a list with Pi and 10^-6 and get a list of decimal numbers as the result. ...
0
votes
0answers
34 views

Handling a matrix with components greater than machine precision

I have four quantities stemming from a 4th order differential equation. I can represent these as a vector which is a product of a 4X4 matrix $$ M=\left\{v,\frac{\partial v}{\partial x},\frac{\partial ...
1
vote
0answers
110 views

Problem setting boundary conditions with NDSolve [closed]

I have the following system of PDEs for which I have given parameters $\gamma, \tau$ and $\mu$, $$\begin{align} T_t = &\ \gamma\,(L +\tau F-T)\\ F_t = & -F_x-(F-LT)\\ L_t = &\ \mu L_{xx}+...
3
votes
1answer
107 views

Fast evaluation of a function in many points

I need to feed to an external program a number of points (in Complex128 format) generated from the numerical evaluation of some function, e.g. $e^{i \vec{k}\cdot\...
0
votes
0answers
37 views

Multi-Precision [duplicate]

I have read in some numerical Laplace inversion papers that we can take advantage of multi-precision environment in Mathematica , Maple and etc.Can someone please explain it for me why it is not ...
2
votes
1answer
89 views

FiniteDifferenceDerivative of complex function in 2D--bug?

I want to compute partial derivatives of complex functions via finite difference approximation on two dimensional grid using NDsolve`FiniteDifferenceDerivative ...
1
vote
1answer
76 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 NDSolve....
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 ...
0
votes
1answer
114 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 ...
-2
votes
1answer
85 views

Tricky ellipse problem [closed]

I have this equation and I need to show it is en equation of ellipse, could anyone help me? 5x^2 - 4xy + 5y^2 = 21
0
votes
1answer
45 views

Strange eigenvector behaviour for matrix with large numerical values

I'm trying to compute the eigenvectors of a matrix with large numerical values $$ \left( \begin{array}{ccccc} 0 & 1.\times 10^{18} & 100 \text{X} & 0 & 1.\times 10^{11} \text{X} \\ ...
2
votes
2answers
174 views

Maximizing over an integral with a single parameter

There is probably a neat approach to solve this problem...but can't get to it at the moment. How do you maximize an integral with respect to a single parameter? My code below produces error messages. ...
1
vote
1answer
105 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
95 views

Help with findroot optimization

I'm trying to solve the set of coupled equations $$\frac{-N -2( \lambda + N(\frac{\beta}{\epsilon}-\lambda))\upsilon_l + N \upsilon_l^2-2(N-1)\gamma\upsilon_l^3}{\gamma-2\lambda\upsilon_l^2+\gamma\...
0
votes
2answers
60 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
1answer
75 views

Implementing AiryAiPrimeZero function

There are some functions implemented in the Wolfram Language related to Airy functions. For example, AiryAi, AiryAiZero or ...