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

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10
votes
0answers
562 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 $$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
4
votes
1answer
906 views

Symbolic integration in the complex plane

Context While answering this question, I defined (symbolic and numerical) path integrations as follows ...
3
votes
0answers
400 views

Numerically solving PDE with high precision

I want to numerically solve the PDE $\partial_t u(t,x)=c\partial_x u(t,x)+(mx-l)u(t,x)$ with some initial and boundary conditions and given parameters $c$, $m$ and $l$. Consider the code ...
7
votes
1answer
1k views

Is Abs[z]^2 a bad way to calculate the square modulus of z?

For a numerical quantity z, Abs[z] returns the square root of the sum of the squares of the real and imaginary parts of ...
8
votes
1answer
959 views

Implementation of Incomplete Fermi-Dirac Integral in Mathematica

I'm working on a special algorithm to implement a more accurate effective mass calculation for hole carriers in silicon in Mathematica. This rather involved algorithm uses incomplete Fermi-Dirac ...
9
votes
1answer
215 views

RandomReal closed on left & open on right?

I have a number of algorithms that depend on uniform random reals in half-open intervals such as $[0,1)$. In particular, I need a (pseudo) random-number generator that produces machine-precision ...
3
votes
1answer
199 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 ...
4
votes
1answer
821 views

Mathematica NDSolve and 'Compile'?

Since the consensus is usually that NDSolve speeds fares badly against compiled code such as c++ ODE solvers using GSL say, is it possible to make up for this lag ...
12
votes
2answers
429 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 ...
1
vote
1answer
300 views

Why is NDSolve solving in term of two 1st order ODE slower than 2nd order?

As mentioned in the documentation for NDSolve it's often convenient to reduce a 2nd order ODE to a system of first order equations. When I do this however I seem to see a significant speed reduction ...
2
votes
1answer
728 views

NDSolve runs out of memory

I need to solve a second order ODE numerically. The ODE depends on two parameters (a,b). Things work fine when 'a' is small, but for large 'a' the solutions are oscillating rapidly and Mathematica ...
1
vote
1answer
453 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 ...
11
votes
3answers
3k views

NDSolve with Euler method

I want to solve this equation with NDSolve[] using the Euler method: x'[t] == 0.5*x[t]-0.04*(x[t])^2 with initial condition ...
14
votes
1answer
1k views

Poisson solver using Mathematica

I am looking for some help with a Poisson solver I am writing in Mathematica. The code is quite long with Arrays plugged in, so the full details can be found at http://pastebin.com/uSrSDcW6 I am ...
2
votes
1answer
213 views

Numerical comparisons of matrices

I have a matrix which should be equal to a null matrix. However due to the numerical precision, a brutal equality test with a matrix initialized with zeros does not work. How should I perform the ...
1
vote
2answers
103 views

NSum generates a warning message when getting the sum of a list

I know what I'm doing can be done with Total: a = Range@3; Total@a And if I simply choose ...
10
votes
1answer
898 views

How do I find all the solutions of three simultaneous equations within a given box?

Sometimes, one needs to find all the solutions of three simultaneous nonlinear equations in three unknowns $$\begin{align*}f(x,y,z)&=0\\g(x,y,z)&=0\\h(x,y,z)&=0\end{align*}$$ within a ...
19
votes
3answers
896 views

Can Mathematica Handle Open Intervals? Interval complements?

Open Intervals Following up on this question, I was wondering whether Mma can handle open intervals. For example, the union of the intervals, $$1<x<5$$ and $$5<x<8$$ should not ...
2
votes
1answer
435 views

How to solve simultaneous equations faster with Compile?

I have large 6x6 matrix Uwhich is a multiplication of 15 rotational matrix. All of the elements are Sin\[theta] and ...
5
votes
1answer
741 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
365 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
334 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 ...
23
votes
1answer
746 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
280 views
9
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
957 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
1k 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
401 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 ...
34
votes
3answers
2k views

Identifying critical points/lines 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
846 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\ ...
21
votes
3answers
616 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
191 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 ...
12
votes
1answer
1k views

AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
8
votes
1answer
401 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
113 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
3k 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
279 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
127 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 ...
11
votes
3answers
1k 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
269 views

Converting to machine precision

There are multiple ways to convert an expression to machine precision, for example: ...
16
votes
5answers
689 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
218 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 ...
5
votes
0answers
430 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
411 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 ...
17
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
449 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
472 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
877 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
462 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 ...