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

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4
votes
1answer
249 views

Find lengths of contours in a ContourPlot

I am trying to find the lengths of different contours in the following plot: It is a complicated piecewise function evaluated on the unit disk. I am hoping there is an easy, generalized way to ...
2
votes
1answer
545 views

Different Poincaré maps for same Equation

I've seen the Wolfram Poincaré example. I'd like to modify this sample in order to have a list of Poincaré maps. In the example the event is captured only when ...
0
votes
0answers
115 views

complicated Numerical Integration, FEM application

I am trying to calculate a 2d Integral which has another 2d integral in the integrands. here is the setup: ...
0
votes
1answer
219 views

Scaling the time axis of an interpolated function (as in a solution from NDSolve)

I'm wondering how I can change the units of the x (time) axis when plotting a solution from NDSolve. I have obtained three solutions to a system of differential equations, all of which exist over the ...
4
votes
1answer
439 views

Why IntegerPart[x/(x/2)]=1?

Consider this code x = 0.109354682484; IntegerPart[x/(x/2)] (* 1 *) Precision[x] (* MachinePrecision *) Why does it give 1 ? Version number: 9.0 on Mac 10.9.2 ...
5
votes
1answer
106 views

How to enforce numerical precision throughout a package

I developed a big package that does quite a bit of numerics. Is there a way to enforce that all numerical computations are done with a pre-defined accuracy? For example, can one use something like ...
1
vote
1answer
309 views

Discrete sampling of interpolating function returned by NDSolve

When solving an ODE with NDSolve, Mathematica returns an interpolation function. I need a discrete sampling of this function however. Naively, I can write this as (example): ...
0
votes
1answer
588 views

Heat Transfer equation by numerical methods

I want to solve the following heat conduction equation using numerical methods: D[u[x, t], t] -alpha*D[u[x, t], {x, 2}] == 0 u[x, 0] == 1/(1 + x^2)^0.25, u[-10, t] == u[10, t] == 0, ...
1
vote
0answers
53 views

How to find discretezation error of NDSolve

Is there a way to find out how large the truncation, round-off, and other errors that occur from discretizing a differential equation are while using the default settings in NDSolve? Or would I have ...
1
vote
2answers
294 views

Mathematica can't minimize a function

Mathematica seems not to be able to minimize this univariate function over integer arguments, $r>2, r \in \mathbb{Z}$. ...
1
vote
1answer
150 views

Numerically solving an ODE for a parameter

My equation is as follows: sol = ParametricNDSolve[{(f'[r]^2 - 1) f'[r] r == 6.2 (f'[1])^2/1000, f[1] == a}, {f}, {r, 1, 3}, {a}] where the function ...
5
votes
3answers
298 views

Increasing the precision of a calculation

Clearly I have misunderstood how to do this: I seem unable to understand how to get more digits out of a calculation and I can't see why - the following piece of code illustrates the issue. ...
2
votes
2answers
93 views

Forcing RecurrenceTable + NIntegrate to evaluate lazily

I have a recurrence relation that grows exponentially if expressed in closed-form. I need to integrate this function. If I plot it, I think Mathematica evaluates the recurrence numerically at every ...
1
vote
2answers
201 views

NDsolve with variable end-point

I want to plot the solution a coupled ODEs as a function of the end point only. Mathematica code: ...
2
votes
1answer
228 views

Fourier Transform Help

I'm trying to do a Fourier Transform of the following Data, but I'm completely stuck. Here's what I've done so far: ...
4
votes
2answers
268 views

Floating point addition not associative

Can anybody explain the following behavior? x = 0.2 + (0.3 + 0.1); y = (0.2 + 0.3) + 0.1; x == y (* -> True *) But actually the variables do not exactly ...
3
votes
1answer
504 views

N[number, 100] does not give 100 decimal places [duplicate]

Please look at this computations: a = N[Sqrt[2], 20]; N[a^2, 100] The output is 2.0000000000000000000, which is apparently not $a^2$ to 100 decimal places. ...
1
vote
1answer
264 views

Perform FindRoots on Function Evaluation Containing RootSearch

I am using Ted Ersek's RootSearch function in Mathematica 9.0 (http://library.wolfram.com/infocenter/Demos/4482/) to create a function that I am using for graphing. ...
-1
votes
1answer
394 views

Multiple NIntegrate (again)

Basically I have the same question as here: Multiple NIntegrate but since I don't have enough "reputation" I cannot comment there. I want to solve the following multiple Integral numerically at given ...
5
votes
0answers
152 views

NMinimize seems to call function with the same values multiple times

I have to minimize a function where the evaluation of one parameter set takes very long (around 5sec) and discovered alongside, that NMinimize seems to call this ...
1
vote
1answer
399 views

Numerical saddle point problem of a function of many variables

I want to find the following saddle point of the function of 10 variables: . I am not able to find the stationary points by setting the first derivatives to 0, so I need do optimize the function ...
3
votes
2answers
191 views
9
votes
1answer
405 views

Is there a way to see the result of NIntegrate's symbolic preprocessing?

NIntegrate can do a number of different types of symbolic preprocessing on the integrand before starting the numerical calculations, including changes of variables. ...
0
votes
1answer
774 views

How to use NIntegrate in a function using parameters from a list

I would like to use NIntegrate in a function with some parameters from a list. I simplified my problem for this forum. The list of parameters is as follows: ...
0
votes
1answer
687 views

Boundary Value Problem

I have to solve this boundary value problem: $$\frac{\mathrm{d}e_{3x}}{\mathrm{d}l}=(M_0+F_{0z}x-F_{0x}z)e_{3z}$$ $$\frac{\mathrm{d}e_{3z}}{\mathrm{d}l}=-(M_0+F_{0z}x-F_{0x}z)e_{3x}$$ ...
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 ...
1
vote
1answer
229 views

FindMaximum inconsistency

The code below seems to work for n<11. But for n=11, and above, it outputs newa then just outputs "beep" sound. WhyTheBeep says "The kernel Local has quit ...
3
votes
1answer
216 views

Why to do parentheses change the results of a calculation?

I'm getting results that are sensitive to where I place parentheses with respect to operations that are associative1 (and should thus be insensitive to such placement). For example, if I define2 ...
4
votes
2answers
304 views

Graphing convolutions of user defined functions

I am a statistician who is very new to Mathematica. Ultimately I would like to be able to graph convolutions of arbitrary user defined functions. But I can't as yet obtain values of such ...
0
votes
2answers
302 views

FindMinimum gets confused by If[…]

I'm confused by why the following doesn't work. I'm trying to numerically minimize a function that has an If statement in its definition, as follows: ...
1
vote
2answers
1k views

Kramers Kronig Relation for Phase and Complex Reflectivity

I am a new user to Mathematica and I have been trying to figure out how to find $\Theta(\omega)$ from my 'experimental' values of energy and $\ln(\sqrt{R(\omega)})$ (I am just running a simulation, ...
4
votes
0answers
138 views

Tools for Stability/Automatic Error Analysis in Mathematica

I have a longer analytic expression in several variables containing special functions and others. Does Mathematica bring tools - or are there any packages - to examine the stability when I evaluate ...
27
votes
3answers
825 views

How to flush machine underflows to zero and prevent conversion to arbitrary precision?

I'm working on some pretty intense computation in Mathematica; when my code started running slowly, I tracked the source of the problem to Exp[]. I need to ...
2
votes
2answers
384 views

Can Mathematica identify formulae or sequences of numbers?

Can Mathematica suggest what a formula means? For example if I input $$\sum_{i=0}^n i$$ can it infer that this is a sum of integer values from $0$ to $n$? Or if I enter $0,1,1,2,3,5,8,13$, can ...
2
votes
1answer
146 views

Decomposing a diagonal positive real matrix

I would like to 'decompose' a diagonal positive real matrix $E$ of rank $D$ onto $\sum_{i=1}^{D}c(i)N^i$: $$E = \left( \begin{array}{ccc} 0 & & & \\ & a & & \\ ...
3
votes
3answers
313 views

How can I find the sum of the even digits of a number of all elements of a list?

Let $E(n)$ denote the sum of the even digits of $n$. For example, $E(123456789) = 2 + 4 + 6 + 8$. I tried a = IntegerDigits[123456789] and ...
1
vote
1answer
190 views

Problem to solve an integral equation [closed]

I am new to Mathematica. I am trying to numerically solve for C in the following equation: $\begin{equation} \begin{array}{lcl} -\int_0^\infty (5000000+100000 x+ C)^{-1} ...
3
votes
0answers
133 views

Understanding NDSolve::ndsz

I'm working on a largeish system of differential equations where I encounter the NDSolve::ndsz step size is effectively zero; singularity or stiff system suspected ...
4
votes
3answers
510 views

First 10 digits of $\pi$ without rounding

I need to have $\pi$ with an accuracy of $10$ digits. My first guess would be N[Pi, 10] However, this rounds to the last digit instead of just chopping of any ...
2
votes
1answer
98 views

Convert Integer to Numeric with Replacement rules

I have a long list of triples, each looking something like {AGO, 1988, 2345.23}. Some of these, however, have an integer in the third spot, like this: ...
9
votes
4answers
438 views

Numerical instability in cosh and sinh - integral functions [duplicate]

I'm trying to calculate the function: CoshIntegral[x] Sinh[x] - Cosh[x] SinhIntegral[x] Unfortunately Mathematica seems to hit a point (x~20) and things become ...
1
vote
0answers
725 views

DSolve 2nd Order Coupled Partial Differential Equations

I am trying to use Mathematica to solve 2 coupled differential equations. My equations are of the form \begin{equation}\ddot{x}_i + A_{il} \partial^l A^{jk} ( \dot{x}_b \dot{x}_c - y_b y_c ) =0 ...
6
votes
3answers
364 views

Finding the square root of a squared number?

Taking the square root of the square of a number Variable set to a real value I'm wondering why these examples a = -4.3; Sqrt@a² Sqrt@(a^2) Sqrt[a^2] Sqrt[a²] ...
1
vote
1answer
320 views

NSolve with numerical function

I would like to solve numerically an equation which involves a numerical function constructed by fitting some data: ...
1
vote
1answer
128 views

How do I get Nsolve to work with hyperbolic functions?

This is a rather simple numerical solution, but it simply doesn't work. Does anybody have a solution? NSolve[x - Sinh[x] - 1 == 0, x] NSolve::nsmet: This ...
0
votes
1answer
108 views

Removing numerically vanishing complex part within NDSolve

I am using functions that are only well-defined for real values (e.g. HeavisideTheta) within NDSolve. Internally ...
12
votes
4answers
642 views

Why is Poisson Random Deviate Generation so slow?

I am generating Poisson deviates for some numerical work. Mathematica 9.0.1 is very slow in generating these random numbers, as can be seen below. ...
2
votes
4answers
285 views

Padding and formatting within BaseForm

I find using BaseForm to be a little tricky. For example, if you use BaseForm and then do some additional operation all the numbers turn back into base 10, so you have do BaseForm as the "last step". ...
2
votes
2answers
226 views

Incorrect numerical derivative of function that uses FindRoot

I am trying to plot the derivative of function g[x] below where g[x] is defined as the root of another equation. However, I am ...