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

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4
votes
1answer
578 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 ...
1
vote
3answers
354 views

equation solving problems

I have some equation: $$ veq=-2-lr-l^2r+2(r+ir^3\omega) v' + (-2+r)r^2v'^2 + (-2+r) r^2 v''==0 $$ or in Mathematica form: ...
8
votes
1answer
301 views

ReplaceAll[] and Limit[] don't give correct results for this expression under extreme variables [duplicate]

Possible Duplicate: Funny behaviour when plotting a polynomial of high degree and large coefficients 1/x^2 + (3 + x)/(6 (1 - Exp[x] + x)) ——This is a ...
15
votes
0answers
590 views

Fast Spherical Harmonics radiative transfer

This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me. I am using ...
5
votes
4answers
2k views

Numerical Differentiation using 1500 data points

I have a set of 1500 data points (which are some energy eigenvalues) corresponding to a parameter H0 (which represents magnetic field. H0 values are equispaced going from $-3.0$ to $3.0$ in steps of ...
2
votes
4answers
277 views
8
votes
2answers
2k views

How to discretize a nonlinear PDE fast?

I wish to numerically solve the following PDE. Although there are some complete discussions for solving PDEs in tutorial/NDSolvePDE, there is no hint for the nonlinear case by discretization. Thus, I ...
1
vote
1answer
811 views

Problem while solving system of two second order non linear coupled differential equations using NDSolve function

I am a completely new to Mathematica, and I am sorry if this question is dumb. I have to solve a system of two second order non linear coupled differential equations (that I got from the Lagrangian ...
16
votes
2answers
985 views

Higher order periodic interpolation (curve fitting)

I have a list of points in 3D, and I want to get a smooth interpolation or curve fit (it is more for illustration) of these points such that the first and second derivatives at the start and end ...
13
votes
1answer
394 views

What strategies can I use to evaluate a limit when Limit[] returns unevaluated

I'm trying to find the following limit using Mathematica: $$\lim_{N\to\infty}\sum_{k=1}^N\left(\frac{k-1}{N}\right)^N$$ The problem is taken from here and is known to converge to ...
27
votes
5answers
2k views

Identifying critical points of 2/3D image/cubes

Upshot I am interested in identifying critical points of a 3D field/cubes (maxima, minima, tube-like and wall-like saddle points) and 2D field/image (maxima, minima, saddle points). I.e. the ...
3
votes
2answers
757 views

Numerically Solving two dependent Transcendental Equations

I need to solve a system similar to the following (Except it is quite large. Solving this ought to do the job): $$ \tan[2f(t)] = 1+ t^2\ $$ and $ f(t) $ is $ k $, such that$$ \tan[2kt]-(1+k^2) = 0\ ...
20
votes
3answers
557 views

Computing polynomial eigenvalues in Mathematica

MATLAB offers a function polyeig for computing polynomial eigenvalues, which appear, for instance in quadratic eigenvalue problems (see here for some applications) such as: \begin{equation} ...
3
votes
0answers
172 views

LeastSquare Solution for the Continuous Time Lyapunov Equation

I have been working with a problem which involves solving the continuous time Lyapunov equation $$A R + R A^\top = G$$ for the symmetric positive definite matrix $R$. Here $A$ is real, invertible ...
11
votes
1answer
894 views

AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
8
votes
1answer
370 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 ...
4
votes
1answer
110 views

NExpectation not up to expectations with Boole or Conditioned

Context I am interested in computing numerically the number of extrema at a given threshold for random fields. These numbers are expectations of MultinormalDistributions. Problem This integral ...
27
votes
2answers
2k views

Efficient Langevin Equation Solver

This question is not about good algorithms for solving stochastic differential equations. It is about how to implement simple codes in Mathematica efficiently exploiting Mathematica's programming ...
0
votes
1answer
239 views

Problem with Eventlocator Method for NDSolve

I want to solve the ode and plot the solution v[x] for different values of parameter a where ...
1
vote
2answers
122 views

How do I prevent this precision exception?

I have the following as the first step to a sequence. x = 2 - GoldenRatio; Ceiling[x + x^(1/2)] It gets a precision exception. The value is correct, but I would ...
9
votes
3answers
850 views

How do you round numbers so that it affects computation?

I'm trying to make a demonstration of how rounding to different numbers of digits affects things but I can't find a way to round numbers to a specified number of digits. The ...
10
votes
1answer
241 views

Converting to machine precision

There are multiple ways to convert an expression to machine precision, for example: ...
16
votes
5answers
614 views

Is this the most efficient way to round approximate integers to integers while leaving other Reals untouched?

This might seem like an overly simple question, but I need to specify custom plot tick marks as integers (no trailing decimal point) if they are approximately integers, but not if they are not. Using ...
8
votes
1answer
207 views

SetPrecision within Block

I am reading Mathematica Cookbook, chapter 1. Author gives two examples, with the following explanation You can control precision within a complex calculation (without using ...
4
votes
0answers
350 views

Semidefinite Programming

I want to solve a numerical optimization problem using semi-definite programming. Is there a package or add-on that equips mathematica with this functionality?
5
votes
1answer
375 views

Tridiagonal symmetric matrix eigenvalue using bisection

I know that Eigenvalues is already quite well implemented in Mathematica, nor am I foolishly trying to improve on it. In order to improve my programming skills, I ...
16
votes
5answers
2k views

The difference between 0. and 0

I have a function for which 0 is a special case: f[A___, 0, B___] := 0 But since I am doing numerics, sometimes in the course ...
2
votes
2answers
405 views

Unexpected result of summation

I wrote small module that gives me incorrect output-set, it should be a single number! I don't understand what went wrong. This is the form of summation used: $$\frac{1}{2} (b-a) \sum_{i=1}^n ...
2
votes
2answers
396 views

Quickly differentiate and evaluate a function of several variables

How can I differentiate a function with respect to several variables and evaluate it at the same time ? I want to specify also the variable index that I want to differentiate and the number of times I ...
5
votes
3answers
786 views

Solution for equation system with piece-wise defined functions

As I could swear this worked just yesterday, I am probably just doing something stupid here and I am sorry to bother you :) I am trying to find the point where a curve crosses a line. In this case, ...
7
votes
4answers
419 views

Distances between points in periodic cube

How can one implement more efficiently/elegantly/memory savvily the following function which returns a matrix of all Euclidian distances between points in 3D within a cube of width ...
34
votes
2answers
829 views

Is it possible to make Mathematica reformulate an expression in a more numerically stable way?

I'm writing a numerical optimization, and I'm having a problem with an expression of the form $$ e^{-t} (1+\mathrm{erf}(t)) $$ The overall shape of the function looks correct, but when $t$ is small, ...
0
votes
1answer
120 views

Numerical rule evaluation -> {True, False} to deviation of target equation

I solve some equations numerically with FindRoot[] returning a quadruple {1,2,3,4}. Because the solver sometimes do not find any roots depending on parameterization of these equations I select only ...
6
votes
1answer
273 views

Numerical problems with calculation of function

I have a problem with a calculation which I try to do with Mathematica (8.0.1). I have the following function which describes a cone (with half opening angle ...
15
votes
6answers
4k views

About multi-root search in Mathematica for transcendental equations

I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range? Perhaps ...
13
votes
3answers
1k 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 ...
4
votes
3answers
589 views

Output of NonlinearModelFit differs from the correct result

I'm having a bad time dealing with the NonlinearModelFit in Mathematica 8, since the result given is a bit imprecise. An example is given on potential regression, ...
0
votes
1answer
294 views

Tabulating Numeric Approximation

I was wondering how to approximate or tabulate values for this numeric approximation: It is the following: The confusing part is how to implement the subscripts in mathematica. $y_{i+1} = (t_i - ...
8
votes
2answers
2k views

Numerically obtaining the inverse Laplace transform of data

I have been using several Mathematica packages to do numerical inverse Laplace transforms on known (expressible in closed form) expressions, $\tilde{f}(s)$. I am now being confronted with the more ...
12
votes
3answers
2k views

Solving a Volterra integral equation numerically

I would like to solve for $P(t)$, in Mathematica, a Volterra integral equation of the 2nd kind. It is: $$P(t) = R_0(t) + \int_0^t P(t') R_0(t-t')dt'$$ I know the function $R_0$ and would ...
8
votes
2answers
640 views

Number of iterations in NSolve

In Excel's solver, one can define how many iterations are to be done, to one's liking. I am wondering if this is possible to do with NSolve in Mathematica? Code ...
32
votes
6answers
4k views

Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)

Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$. When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], Mathematica gives the ...
12
votes
4answers
1k views

Numerical underflow for a scaled error function

I calculate scaled error function defined as f[x_] := Erfc[x]*Exp[x^2] but it can not calculate f[30000.]. ...
17
votes
6answers
1k views

Annoying display truncation of numerical results

I have a lot of data to inspect. An example of a number in my program is 123.189094 This gets displayed as 123.189 ...
7
votes
1answer
737 views

Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
17
votes
2answers
490 views

Obtain approximate Hessian using FindMinimum

According to the documentation, when FindMinimum is told to use the method "QuasiNewton" on a unconstrained problem, it uses the ...
12
votes
1answer
2k views

What method does NDSolve use for solving PDEs?

What is NDSolve's mode of operation? I use it to solve partial differential equations and never gave it too much thought. Recently, I came across this question. ...
12
votes
2answers
356 views

Wrong computation with N

I was trying to solve this problem using Mathematica 8.04. I did this: ...
17
votes
1answer
591 views

Funny behaviour when plotting a polynomial of high degree and large coefficients

I am trying to plot a polynomial of degree 29 on the domain [0,1], with fairly large coefficients: ...
25
votes
2answers
960 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 ...