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

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5
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2answers
152 views

Evaluate numerically an extremely small number

How to evaluate numerically $e^{-4 \cdotp 10^{35}}$ in the form $0,a_1a_2...\times 10^{-n}$ ...
5
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3answers
250 views

Finding the conditions for degenerate solutions to a cubic equation

I have a cubic equation (corresponding to the band structure of a physical system) given by w in the code below. ...
5
votes
4answers
178 views

RegionMember with some tolerance?

Can I specify some tolerance for the new geometric-computation function? RegionMember[Line[{{0, 0}, {1, 0}}], {.5, 0}] (* True *) While: ...
5
votes
1answer
116 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, ...
5
votes
1answer
203 views

Is there an alternate way to calculate beyond the memory limit of the home edition?

I bought the Home Edition of Mathematica online 0.5 G of memory and costs \$150 per year. When I calculated the median of outputs from $[0,1]$ with an interval of $.000001$ I ended up with the ...
5
votes
1answer
1k views

Symbolic integration in the complex plane

Context While answering this question, I defined (symbolic and numerical) path integrations as follows ...
5
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3answers
1k 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, ...
5
votes
1answer
75 views

Finding the correct boundary conditions to a specific problem

I want to reproduce the following problem in the figure: $$\phi''+c\phi'\sqrt{m^2\phi^2+\phi'^2}+m^2\phi=0$$ where $\phi=\phi(x)$ with $x \in (-\infty,\infty)$, $c=\sqrt{3/2} \ $ and $m=0.2$. ...
5
votes
1answer
85 views

Can Someone Please Explain Internal`$SameQTolerance?

If I input Internal`$SameQTolerance (* output = 0.30103 *) which is the approximation of Log[10,2], or ...
5
votes
2answers
567 views

How can I numerically solve for fractional functions and fractional derivatives?

I would like to plot fractional functions. Say, $f(x)=\sin^{(1/2)}(x)$. By that, I mean that $f(f(x)) = \sin(x)$. Similarly, I can define a half-derivative to be an operator $H$ such that $H[H[f(x)]]...
5
votes
1answer
371 views

Accurately evaluating the hypergeometric function

As part of another problem, I am working to evaluate hypergeometric functions such as Hypergeometric2F1[1, 1, n, -1] for large $n$. I am hoping to obtain at ...
5
votes
1answer
107 views

Compilation, square roots, and integers

After looking at this question, particularly this answer, I wrote my own performance test, using the two functions ...
5
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2answers
325 views

NDSolve in Mathematica won't use all the cores avaiable

When I solve a system of differential equations in Matlab, the task manager shows that all the CPU cores are in use. This is not true when I solve the same system in Mathematica. I have six cores. ...
5
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1answer
88 views

Why is NHoldFirst not propagated to symbolic derivatives?

I encountered a nasty problem that N cannot evaluate expressions containing a symbolic Derivative of a multi-parameter function ...
5
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2answers
1k views

Can the CholeskyDecomposition function in Mathematica be made to work on non-symmetric matrices?

The CholeskyDecomposition[m] function in Mathematica requires a symmetric and positive definite matrix m. For instance, the ...
5
votes
1answer
119 views

Determining the range of parameters that yield real values for a certain NIntegrate form

I have specified just one set of $s$ and $g$ values that yields a real value for the NIntegrate below. It is possible that some $s,g$ combination can give rise to ...
5
votes
1answer
76 views

ComplexInfinity for a convergent product

The infinite product involving the ratio of (n^2)! to its Stirling approximation ...
5
votes
1answer
202 views

NDSolve - sampling for result during the computation

I am using NDSolve for a Langevin dynamics problem. I want to the know long term behaviour of my system ($t>1$) but it has to be simulated with very small time steps ($dt\sim 10^{-9}$). An example ...
5
votes
1answer
696 views

p-iteration algorithm to solve Lambert's problem for interplanetary trajectories

I've been reading up on using the p-iteration method to solve Lambert's problem for choosing the correct interplanetary trajectory between two planets given the ...
5
votes
1answer
557 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 ...
5
votes
1answer
281 views

Trouble with shooting method for a 4th-order stiff ODE

The ODE I need to solve is $$\left(y^3y^{\prime\prime\prime}\right)^\prime+\frac{5}{8}xy^\prime-\frac{1}{2}y+\frac{c}{y}=0$$ where $\prime$ denotes differentiation, $c$ is a constant and $0<c\le1$....
5
votes
1answer
322 views

FindMaxValue specifics

I'm using FindMaxValue to study the distribution of maxima of Abs[RiemannSiegelZ[t]] between consecutive values of ...
5
votes
2answers
147 views

Display All Output Numbers in HEX

How might I modify Mathematica such that I can get the following functionality when working with HEX values. The odd lines are input and the even output. Red values should be the HEX values. ...
5
votes
1answer
578 views

Counting the number of operations performed during a calculation

I need to know how can I count the number of operations performed during a calculation of a CompoundExpression. In some of these expressions there are ...
5
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0answers
72 views

How does Plus work on machine precision Real arguments?

I thought Kahan's summation method would make a nice example for students to use to think about round-off error [W. Kahan, Pracniques: Further Remarks on Reducing Truncation Errors, Commun. ACM 8  (...
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0answers
65 views

How to pass a custom method to a particular option?

In an answer to my question More efficient method to compute moments of the Johnson $S_B$ distribution, J. M. has come up with a method to compute the moments of the Johnson $S_B$ distribution, which ...
5
votes
1answer
112 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 ...
5
votes
0answers
183 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 ...
5
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0answers
1k views

Numerically solving system of partial differential equation

I am trying to solve a system of partial differential equation with boundary conditions. But I got an error message saying NDSolve::icfail: Unable to find initial ...
5
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0answers
170 views

Numerical solution of Schrödinger-type equation in Mathematica [duplicate]

I want to solve the following differential equation numerically: \begin{equation} i\partial_{t}\psi(r,t)=\left[-\frac{\Delta}{2m}+g\left|\psi(r,t)\right|^{2}+V_{d}(r,t)\right]\psi(r,t) \end{equation} ...
5
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0answers
697 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?
4
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4answers
293 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 ...
4
votes
2answers
354 views

How to make the computer consider two numbers equal up to a certain precision

My problem is that I have a matrix A and the computer says is not Hermitian (self-adjoint). Then I check which elements make A ...
4
votes
3answers
796 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, ...
4
votes
4answers
268 views

How to stop a summation when a variable is small enough?

I meet with a problem. I hope to get an infinite summation of $f1(x)/f2(x)$ which converges to zero. So my code is Sum[f1[x]/f2[x],{x,Infinity}] or ...
4
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2answers
258 views

Rotating an Interpolating Function

I have used the following code to generate eigenfunctions of a PDE: ...
4
votes
3answers
536 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 ...
4
votes
1answer
353 views

How to calculate accurate answer in Mathematica?

I accidentally discovered for myself, that Mathematica outputs inaccurate answer. For instance, if I take $\sin(2 \cdot \pi \cdot 0.5) = 0 $, then in Mathematica it is: But if I calculate it on ...
4
votes
2answers
271 views

Numerical sum does not give consistent results

Consider the function ...
4
votes
4answers
599 views

How to find the maximum of a function on a set of discrete points?

How to find the maximum of a function on a set of discrete points? For example, what is the best way to find the maximum of ...
4
votes
1answer
497 views

How can I deal with a non-numerical value for a derivative at $t = 0$ when using NDSolve?

I want to solve two coupled equations with NDSolve, ...
4
votes
2answers
806 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
2answers
83 views

N not behaving in the way I expected it would

I'm trying to use the N function to find the percent error between a function and a rounded value of that function. The code looks something like this. ...
4
votes
2answers
1k views

Numeric calculation of Hessian

I want to calculate the Hessian matrix for a function that can only be evaluated numerically. So far, I have the following (where f is just for testing): ...
4
votes
1answer
210 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. ...
4
votes
1answer
192 views

Unexpected results from trying to solve Laplace's equation

I am trying to find the solution to Laplace's equation: $\dfrac{\partial^2 u}{\partial x^2}+\dfrac{\partial^2 u}{\partial y^2}=0$ over the following region of space: the vertices of the triangle ...
4
votes
2answers
255 views

Problem with machine number precision in compiled functions

When I compile a very big function and give it input the function returns error. I realized that this is because the value of the function becomes smaller than the smallest machine number. Is it ...
4
votes
1answer
440 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 ...
4
votes
2answers
316 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 ...
4
votes
2answers
751 views

Why doesn't FindRoot work correctly?

I'm trying to find the roots of the following equation: I need to find λs for different values of ξ. I know that for all ...