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

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3
votes
0answers
47 views

Numerical integration: complicated 2D integral seems to be poorly estimated

In the course of some physics research I've been working on, a very annoying integral has appeared that I'm having difficulty evaluating numerically. Any help you could offer would be greatly ...
0
votes
1answer
90 views

Writing a Code to plot a function that includes a double integral [closed]

I am trying to write a code in Mathematica. Here are my steps: F[u_] = Some nontrivial and long expression in terms of u; Umax[x_, y_] = Some expression in terms of x and y; W[x_, y_] := integral ...
1
vote
2answers
99 views

Plot a bunch of lines in 3D from point data

I have a 12*25 array, wherein each entry is of the form $\{x,y,z\}$. So 12 different $x$ values, 25 different $y$ values and 12*15 $z$ values in all. I'd like to plot 12 curves of various $x$ values ...
8
votes
3answers
199 views

Why is (-1.)^2. a complex number

Why (-1.)^2. in Mathematica returns a complex number? It looks like in both C and Fortran it returns 1. Why does Mathematica behave differently than the other ...
6
votes
4answers
216 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: ...
15
votes
2answers
368 views

Why is my data 10 times slower than random data when doing matrix multiplication

I have some data generated from some program, and it appears that matrix multiplication on these data are about 10 times slower than on some random data: ...
1
vote
1answer
65 views

Efficient method of raising matrix to a variable power?

I have a $2 \times 2$ matrix $A$, where each element is a 12th order polynomial in a parameter $a$. I need to raise this matrix $A$ to the $-t/T$ power, where $T$ is a known scalar (for this ...
1
vote
3answers
74 views

Speed up NIntegrate, which takes eigenvalues from another function

I have simplified my problem here, in my actual problem the matrix is much bigger which makes it impossible to find eigenvalues analytically. So, I chose standard BCS problem (2x2 matrix) to ...
2
votes
1answer
72 views

How to make N apply to exponent?

For example, I want to covert y+Sqrt[x] to y+x^0.5, where y and ...
1
vote
2answers
163 views

NDSolve with Explicit, Implicit Euler and Trapezoidal method

I am using Mathematica 9.0 both on Linux and Windows and I would like to integrate the Van der Pol equation numerically using various techniques such as Explicit and Implicit Euler and Trapezoidal ...
2
votes
2answers
74 views

WorkingPrecision causes issue in the NIntegrate

I really can't figure out why my code sometimes is not working. My integrals involve two variables (k and kz). The integration ...
1
vote
0answers
60 views

The problem (time) caused by ?NumericQ

In here, I asked a related (similar) question. Using ?NumericQ seems have slowed down the entire calculation. But I now have a more serious problem: ...
20
votes
3answers
416 views

Real Numbers in the Wolfram Language

Epilog: Much of the discussion in the answers below revolves around the distinction between Real as a data type and real numbers as a domain or class of numbers (irrespective of the form in which ...
1
vote
3answers
79 views

How can I use the command `Minimize` of this trigonometric function? [duplicate]

I want to find the minimum of the function $\sin^6 x + \cos^6 x$. I tried Minimize[{Sin[x]^6 + Cos[x]^6, 0 <= x <= 2 Pi}, x] I got {Cos[2 ArcTan[1 - ...
3
votes
1answer
37 views

How shortening argument test when declaring functions?

When defining some functions which depend in many arguments sometimes we need to include question Q constraints to diminish processing time. My question is simple, there is a way to shorten a long ...
9
votes
2answers
313 views

Water Hammer - Numerically solving system of PDEs

I'm trying to use Mathematica to solve the water hammer effect. ...
1
vote
2answers
107 views

Increasing number of decimal places with FixedPoint

I've tried: In[169]:= newton3[x_] := N[1/2 (x + 3/x)]; FixedPointList[newton3, 1.0] Out[170]= {1., 2., 1.75, 1.73214, 1.73205, 1.73205, 1.73205} Of course: ...
0
votes
2answers
61 views

Iteration of NDSolve

I have a problem with iteration of the result of NDSolve. Namely, the following code works fine ...
4
votes
1answer
91 views

Changing the definition of N: unexpected $RecursionLimit::reclim error

I have some objects represented as follows: Object[data, param] data is a list of numbers, ...
0
votes
1answer
47 views

DSolve for first order nonlinear equation is solution numerical or analytical?

Hi I'm new to mathematica so I may have a somewhat trivial question. my code below solves and plots the results of a first order nonlinear ODE. The solutions mathematica gives me contains & and #1 ...
2
votes
1answer
55 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 where the potential governing the ...
2
votes
0answers
116 views

Volterra integral equation

I have to find an approximate numerical solution for the equation $$ F(x) - \lambda \int\limits_1^{x} \text{d}s \;s^2 F(s) Z(x-s) = G(x) $$ $$Z(s) = (\psi''(1-2\ h\ i\ s)- 0.5 \psi''(1-2\ h\ i\ s))$$ ...
0
votes
0answers
24 views

Why numerical functions can't digest InterpolatingFunction with units?

Answering this question gave me the idea that I must be missing something.. In brief, numerical functions generally 'understand' units: ...
0
votes
0answers
45 views

plotting the stable and unstable manifolds of a difference equation

I have a 2D non-linear system of difference equations for variables x and y defined as follows: ...
0
votes
1answer
160 views

Help Please : Error in plotting the solutions of FindRoot

I want to find the roots of an equation using FindRoot as a function of a real parameter K and then plot the real and imaginary solutions vs. the parameter K. The function I'm trying to find the ...
0
votes
1answer
78 views

Fitting data with inclusion of constraints

How do I find a fit for the dataS (see below) with the constraint that the parameter np is an integer, and that the parameters la+lc = 100. A weak attempt at this is provided below for a specific ...
3
votes
2answers
117 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 ...
1
vote
0answers
27 views

Apparent issue with derivative of FractionalPart

This issue came to my attention from Math.SE: http://math.stackexchange.com/questions/1015325/is-the-derivative-of-x-on-0-1-always-equal-to-1/1015342#1015342 To summarize, it appears that ...
2
votes
2answers
84 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 ...
-1
votes
3answers
200 views

Challenge — Defining an ORIGINAL second derivative function?

UPDATE: I do not want to use the Derivative or D functions. – I began with this definition of the derivative , which resulted in: Limit[ #, h -> 0] & /@ { (f[x + h, y] - f[x, y])/ h. But, I ...
1
vote
0answers
55 views

Symbolic and numeric calculations (and plots) simultanuosly

I use Mathematica to do a bunch of symbolic calculations (integrals, ...). This is good because I found that sometimes, if I plug in numeric values, Mathematica takes much longer. However, sometimes ...
2
votes
0answers
62 views

How can I use 'NIntegrate' to show the error?

I have to compute a very complicated integral, which is a 16-dimension one, so NIntegrate use Monte-Carlo. I have set Method -> "AdaptiveMonteCarlo, when I run ...
0
votes
1answer
59 views

Multidimensional NIntegrate problem of the function decaying as 1/x^2

The function I am trying to integrate is more complicated but I can simply write the function as (I had made a typo error, sorry. The '+' sign in front of the r should be '-'): $f(\omega ) = \int ...
1
vote
1answer
87 views

Why Abs[Infinity] is an element of the real numbers

Element[Abs[Infinity], Complexes] returns False, that's right. But ...
0
votes
0answers
49 views

Handling Accuracy and Simplifying

I have the following problem. I have a system of non-linear equations that I log-linearize around a certain point, let's call it point A, using a function that I ...
1
vote
1answer
60 views

Series expansion of InterpolatingFunction obtained from NDSolve

I am trying to obtain a series expansion of the numerical solution of a differential equation. I encounter difficulties going beyond first-order expansions which I believe might be due to my inability ...
0
votes
3answers
72 views

High-Precision NSolve

I need to calculate the intersection of two curves f1[x_] := ((Zl ρ ) Exp[-x]) f2[x_] := (α k e^2 /x^2) Where ...
4
votes
2answers
91 views

How to speed up Min of DateObjects?

I'm in version 10.0.1 using a Dataset to do some plots and things. For one of the plots I need to get the minimum date of a some filtered set of the ...
1
vote
0answers
34 views

How to make a real number parameter go 2 decimal precision? [duplicate]

I'm new at community and I'm starting with Mathematica. I'm now having a trouble with a very simple problem which for many of you might be really obvious. In documentation ...
0
votes
0answers
113 views

NMinimize ignores constraints

I have a problem with NMinimize - I try to minimize quite a complicated function and use a couple of constraints (the way it is shown in the documentation). Now, ...
0
votes
1answer
88 views

How to find all roots of a complex number [duplicate]

Finding all roots, and I know there are four f them, of this (1 - i)^(1/4) Not only real, but imaginary as well
4
votes
4answers
134 views

RegionMember with some tolerance?

Can I specify some tolerance for the new geometric-computation function? RegionMember[Line[{{0, 0}, {1, 0}}], {.5, 0}] (* True *) While: ...
0
votes
1answer
40 views

Error messages from NIntegrate [closed]

I've been trying to work on some integrals (Actuarial Science, for those interested) but somehow this always returns an error for me. ...
2
votes
0answers
48 views

Number recognition in Mathematica [closed]

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?
5
votes
1answer
163 views

Why does taking advantage of Listable change the results of a numerical computation slightly?

I have two variables: t0, and teta0. The first is computed using several nested sums, the second is computed taking advantage to ...
0
votes
0answers
49 views

Why NDSolve With Orthogonal-Projection Method On Orr-Sommerfeld Equation Does Not Work(?)

I am attempting to solve the Orr-Sommerfeld equation for plane Poiseuille flow with the Orthogonal Projection method within NDSolve. The Orr-Sommerfeld equation is (a "stiff" problem); $\psi''''(x) ...
3
votes
1answer
97 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 ...
5
votes
2answers
114 views

Display All Output Numbers in HEX

How might I modify Mathematica such that I can get the following functionality when working with HEX values. The odd lines are input and the even output. Red values should be the HEX values. ...
1
vote
1answer
63 views

How to set products of small variables to zero

Say I have an expression which contains different product combination of very small variables, say, δA, δB, δC. I want to set all the products and all the ...
3
votes
1answer
66 views

Leave out a term when summing

I'm calculating the Madelung constant $$\alpha = -\sum_{n_1,n_2,n_3}{\frac{(-1)^{n_1+n_2+n_3}}{(n_1^2+n_2^2+n_3^2)^{1/2}}}$$ Where $n_1,n_2,n_3$ are any element in the integer domain and they can't ...