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

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1
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2answers
89 views

Performance in calculating maximum-likelihood- based estimates

My probability density function is a complicated one for which numerical estimation is necessary. Here my pdf: ...
4
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1answer
95 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 ...
0
votes
1answer
64 views

How to force numeric evaluation?

I need to evaluate the PolyLog function at some points, but I'm interested in numeric values. E.g. PolyLog[3, 2.7] works fine, but PolyLog[3, e] just prints the same PolyLog[3, e]. I somehow need to ...
9
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2answers
235 views

Solve a PDE over a region defined by a Bezier patch

I am using NDSolve to find the solution to a PDE over an arbitrary domain. The domain is specified by a Bezier patch. ...
11
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1answer
303 views

Does NRoots own an abstract counterpart? If not, can we write one?

We know when solving linear algebra equations, despite its abstract syntax, LinearSolve is much faster compared to Solve: ...
1
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1answer
122 views

NSolve on bounded domain

I don't expect NSolve[] to be able to obtain all solutions in generalfor example. In principle there should be an algorithm that finds all solution to $f(x)=0$ for ...
7
votes
1answer
139 views

Numerical Integration different in Mathematica version 9 and 10 with same options

I have noted that the same function with the same settings gives me different results in Mathematica version 9 and 10. This involves integrating numerically interpolating functions and so on. Here a ...
0
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2answers
69 views

Derivative after numerical Integration

So I have a function that I want to numerically integrate with respect to temperature, so the integral changes depending on the value of temperature being used as it is one of the bounds. After ...
1
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1answer
59 views

Characterising the set of parameters that satisfy a system of non-linear equations

I am looking for a solution to the following problem and could not find an answer so far. I have a quintic equation, $f(x;a,b,c,\cdots)-x=0$, where $x$ is the variable with respect to which I need the ...
-1
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1answer
74 views

My code of plotting a two-variable function is too slow [closed]

I have a code in which my complicated function to be plotted is F(x,p). I would like to graph it for 5 values of p equal to 10^7, 10^8, 10^9, 10^10 and 10^11 for x values between 0.01 and 0.99. All ...
0
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0answers
141 views

Problem with FindRoot applied to functions

I am having difficulty with the error "is not a list of numbers with dimensions..." when using FindRoot (and other numerical routines in Mathematica) to solve equations numerically when the argument ...
1
vote
1answer
84 views

Wrong generalized eigenvalues of large numeric matrices

I've been working on a toy model of a variational method of a Hamiltonian H with an overlap matrix S. The point is that when H and S are small enough, Mathematica gives the correct eigenvalues (≈ ...
0
votes
0answers
25 views

why i cannot get appropriate number with my custom precision? [duplicate]

why i cannot get appropriate number with my custom precision? In[25]:= N[(1 + Exp[-30])/(1 + Exp[-29.9]), 1000] Out[25]= 1. I expect to see a few digits after ...
1
vote
1answer
107 views

How to properly apply NumericQ or s.th. similar here? - NDSolve inside NMaximize

I wrote a function that numerically solves a given Schrodinger equation and returns replacement rules to obtain the time evolution operator. It looks and is used as follows: ...
3
votes
0answers
148 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
116 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 ...
2
votes
3answers
163 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 ...
10
votes
3answers
267 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 ...
9
votes
5answers
309 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: ...
16
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2answers
421 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
107 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
142 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
78 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
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2answers
352 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 ...
7
votes
3answers
452 views

Implement the Bisection algorithm elegantly and easily

Description: Rencently, I have finished my course Numerical Analysis, so I'd like to implement many algorithm that I have learned from that course.By this practice, I hope that I can improve my ...
3
votes
2answers
146 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
1answer
91 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: ...
21
votes
3answers
529 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
102 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
42 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 ...
10
votes
2answers
988 views

Water Hammer - Numerically solving system of PDEs

I'm trying to use Mathematica to solve the water hammer effect. ...
1
vote
2answers
134 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
104 views

Iteration of NDSolve

I have a problem with iteration of the result of NDSolve. Namely, the following code works fine ...
5
votes
1answer
103 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
59 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
112 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 ...
3
votes
0answers
131 views

Mod[1.2, 0.2] is not equal to zero

I'm new to mathematica but this doesn't seem to make any sence In[1]:=Mod[1.2, 0.2] Out[1]=0.2 Why is it not zero? Edit: This is what I wanted to do: ...
0
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0answers
34 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
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0answers
116 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
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1answer
193 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
97 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
303 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
37 views

Apparent issue with derivative of FractionalPart [duplicate]

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 ...
3
votes
2answers
115 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
224 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
85 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
66 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
83 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
105 views

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

Element[Abs[Infinity], Complexes] returns False, that's right. But ...