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

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1answer
609 views

Minimization problem using FindMinimum. Functional value “is not a real number”? [closed]

This question is a follow-up of another one I asked a few days ago. I followed the instructions given in the answer provided by the user that responded. I modified that answer to solve another ...
3
votes
2answers
217 views
8
votes
0answers
467 views

Dual complex integral over implicit path using contour plot

Context I am interested in doing double contour integral over paths which are defined implicitely. For the sake of debugging, let's assume its $$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
1
vote
1answer
169 views

What do these error messages mean when numerically solving differential equations?

I am using Mathematica to numercially solve the following equations: ...
3
votes
1answer
762 views

NDSolve does not respond

For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
0
votes
1answer
147 views

Alleviating a bottleneck involving a function call with symbolic derivatives

I have a bottleneck problem involving a function call with symbolic derivatives. I don't have much experience with Mathematica (or any dynamic language) and I'm certain that the way I've set this up ...
15
votes
4answers
374 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: ...
0
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1answer
195 views

What is the correct way to use NIntegrate inside the FindMinimum function?

I'm having minor issues with the FindMinimum function when using NIntegrate inside. The functions work perfectly well but I get ...
3
votes
3answers
193 views

How can I name “a[[i]]” the parts of Table “a”? Or how to make Table “a” grow inside FindMinimum?

Let's say I want to minimize a function that uses a Table named a with the Conjugate Gradient Method of ...
6
votes
0answers
120 views

Mathematica 7: “LessEqual::nord:” error when using NMinimize on a real function

I encounter a problem (Mathematica 7) similar to Strategies to avoid LessEqual::nord in NMinimize? but the advised strategies don't work for me. Also, I get different results with different ...
2
votes
1answer
165 views

Mathematica 7: Problems when evaluating Fourier inside a ParallelTable

after I got such a great response for my first question on this site, I'm very encouraged to asked my second one! So here it is, very generally: To speed up a "row-wise" (i.e. 1D) operation on a ...
13
votes
3answers
695 views

Strategies to avoid LessEqual::nord in NMinimize?

When using NMinimize on functions with complex intermediate expressions (but a real end result), quite often one gets the error ...
1
vote
1answer
96 views

Can't see updating performed by NMinimize[…,StepMonitor->(…)] outside of Button in which it's called [duplicate]

I've made a peak-fitting GUI in which I have a "Fit" button that, when pressed, calls NMinimize[...,StepMonitor->(step++)] to minimize a sum of squared ...
1
vote
2answers
470 views

Weird NDSolve behavior with Piecewise (MMA9)

NDSolve in Mathematica 9.0.0 (MacOS) is behaving strangely with a piecewise right hand side. The following code (a simplified version of my real problem): ...
15
votes
1answer
938 views

2D Heat equation: inconsistent boundary and initial conditions

I'm attempting to use NDSolve on a 2D boundary value problem with initial conditions. Upon running my code, I get the following message: "NDSolve::ibcinc: Warning: Boundary and initial conditions are ...
3
votes
0answers
294 views

A is fast, B is fast, but together they're Mathematica-crashing slow?

I'm trying to do something with finding solutions to a quantum mechanics problem with n wells. If there are 40 wells, I need to find the solution to an equation in the form: ...
8
votes
4answers
600 views

Numerical integration of a numeric data available as a nested list

I have some numerical data in the form of a list with the following structure: {...{x,y,z},...} defining a surface z=z(x,y) in a 3D space (x,y,z). The data came from a simulation, and I am ...
9
votes
1answer
934 views

Combined numerical minimization and maximization

I want to numerically calculate the maximum of a function defined by the minimization of another function, like the following: ...
0
votes
1answer
172 views

How could we define a function recursively?

Let us first consider the constructon of the following simple iteration ...
2
votes
1answer
583 views

How to solve equations self-consistently

I want to solve the following equation self-consistently. So, H.u = e.u {{1, d}, {d, 1}}.{u1, u2} = e.{u1, u2} I guess an initial value for ...
4
votes
2answers
331 views

Finding all/most roots of a discontinuous function more consistently?

I have the equation: f[x_]:=α Tan[α*a] - Sqrt[c - α^2] and ideally I want to find all of its positive zeros, given a and c, with variable alpha. The problem is ...
4
votes
1answer
475 views

How can I get Mathematica to allow me to apply FindRoot to an expression that contains NIntegrate?

I am trying to run the following command in Mathematica: FindRoot[NIntegrate[D[f[x], x] / Sqrt[1 - x^2], {x, 0, 1}] - d, {a, 245}] As you might expect, a is ...
-2
votes
1answer
185 views

Problem with solving a differential equation [closed]

I need to solve the following differential equation: NDSolve[{R[r, t], R[r, 0] == r/1000}, R, {t, 0, 30}, {r, 1, 30}] Where ...
2
votes
1answer
467 views

intersection between two curves in Mathematica

I have two curves (drawn from points) in a plane, one is drawn with ListLinePlot and the other drawn with ParametricPlot. How ...
2
votes
1answer
229 views

How can I handle curve singularity in this NIntegrate integration?

Yesterday I asked a question about the non converging integral. Woods told me that it is due to the function which has a singularity along a line which passes through the integration region. (Why ...
1
vote
1answer
379 views

Why does this numeric integral fail to converge?

I have an integral over a region (rpp): ...
1
vote
1answer
196 views

How to calculate an integral of an expression that is determined numerically (in Mathematica)?

First of all, I am fairly new to Mathematica and Stackoverflow, so please feel free to give me any advice whatsoever. I aim to calculate an integral of an expression that has been determined ...
8
votes
1answer
351 views

Converting other C++ classes to MTensor in LibraryLink

Hopefully this will be a quick question + a quick answer: Say I have a C++ (or C) code using LibraryLink. I am using a library that defines a specific matrix class, as many numerical libraries ...
1
vote
1answer
139 views

Seemingly simple optimization problem is slow

I'm trying to generate a demand curve numerically, given a utility function. The function for the demand is defined like so: ...
2
votes
1answer
166 views

Computing derivatives of a moment generating function

Dear Mathematica users, I'm trying to compute higher order derivatives of a moment generating function and then evalutate them in 0 (in order to get some moment conditions for a GMM estimation). ...
24
votes
2answers
780 views

Meaning of backtick in floating-point literal

If I compute, say, 1/3//N, Mathematica displays 0.333333 as the result. When I copy that output to use elsewhere, the paste ...
8
votes
1answer
295 views

Symbolic Integration along contour: branch cut problem?

Context Following this question on path integrals in the complex plane, having defined again a numerical and symbolic integrator along a path as ...
8
votes
2answers
332 views

Precision differences

I run this sum and get the symbolic answer below : Sum[ (1/(k^2 - k) - 1/k^2), {k, 2, Infinity}] $2 - \frac{\pi^2}{6}$ I look up the sequence on OEIS and ...
13
votes
3answers
333 views

Make mathematica treat $e_i^2$ as numeric

With NumericQ[symbol] = True, I can declare that a symbol is numeric. I want the expressions matching: $$e_{\text{i$\_$}?\text{IntegerQ}}^2$$ to be treated as ...
12
votes
2answers
383 views

Preventing Numerical value from being evaluated

I have searched stackoverflow (and comparable pages) for quite a while now (got redirected from there to this specialized stack), and I surrender. I am trying to evaluate an expression that is small ...
0
votes
1answer
279 views

How to build a grid of integrand points and numerically integrate?

If I have some function I know numerically only, say f(x) and each point $x$ takes significant time to compute so I have them all stored in some file as f(1)=0.232423, f(1.1)=0.3243432,....Then is it ...
0
votes
1answer
108 views

Non solutions returned by NSolve. And why does it return both phi and Cos[phi]?

Similarly to this thread NSolve gives additional solutions that don't satisfy the equations! NSolve returns "spurious" solutions, even increasing the working precision ...
4
votes
1answer
199 views

How to solve this trigonometric system of equations numerically?

How can the following trigonometric system of equations be solved numerically? ...
1
vote
1answer
172 views

Why does NSum fail here?

I want to evaluate a sum of integrals; each integral has a pole on the real axis and I handle this via the Cauchy Principal Value $ ...
2
votes
0answers
284 views

Numerically/Analytically Solving a System of Equations

I have $6$ functions $f_i(x,y,z)$, $(i = 1, \ldots, 6)$ in three variables $x,y,z$, and I would like to find a simultaneous instance of these variables, say $(x_0, y_0, z_0)$, such that $f_i(x_0, y_0, ...
3
votes
3answers
527 views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
0
votes
1answer
137 views

Industrial Level Applications. Recipe for mixed notation of equations set

I am working with large (linear) equations set within Mathematica in numerical notation. For example, set from 4056 eq. is solved for a second, no more. There is no doubt, result is great. But even ...
4
votes
1answer
177 views

How do I get a list of digits for a number?

I have this 200 digit number where I want to get the IntegerDigits, but the decimal point is in the way. ...
13
votes
3answers
995 views

Finding a fit to a multi-dimensioned function

I have a model function $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$, and a bunch of data points for which I'd like Mathematica to fit for me. Unfortunately FindFit ...
0
votes
1answer
1k views

Tricks for solving (lots of) coupled nonlinear equations numerically?

I have a system of 6 non-linear (quadratic) coupled equations with 6 complex unknowns \begin{align*} |x_1|^2 + |x_2|^2 + |x_3|^2 &= a\\ x_1 x_4^* + x_3 x_5^* &= b + c i\\ x_1 ...
3
votes
1answer
196 views

Construct DifferentialMatrices and Kernel for LevinRule for this integral and ODE set

I've made a lot of progress on my problem the last few days thanks to all the help I've received on here. I think I'm upto the final step of greatly improving the performance of NIntegrate[..] on my ...
1
vote
0answers
165 views

Parallel linear algebra with arbitrary precision

Is it possible to do parallel linear algebra with arbitrary precision within Mathematica (in a simple manner, as is done for the machine precision)?