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

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2
votes
1answer
327 views

How to make Mathematica try harder to perform symbolic comparisons?

(I suspect this question is a duplicate, but I didn't find a sufficiently similar question with an answer to it.) I'm having trouble with comparisons of symbolic ...
2
votes
2answers
440 views

Strange Behavior of NDSolve

I am trying to evaluate the following ODE numerically: ...
2
votes
1answer
511 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 ...
2
votes
1answer
259 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). ...
2
votes
1answer
983 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 ...
2
votes
2answers
52 views

How do I overcome an Overflow?

I'm trying to calculate entropies for an absolutely giant system by counting states, and this means I have to use some obscenely large numbers. I'm running ...
2
votes
1answer
105 views

NDSolve with two parameters

I was trying to solve a ODE numerically. It has two parameters (w and z0) which I want to vary. The following code gives an ...
2
votes
3answers
153 views

Use NMinimize instead of FindFit for constrained search (of coefficients)

(My problem is more complex, but let us formulate it through this example) I am trying to find the best polynomial approximation to the following function ...
2
votes
1answer
91 views

Singularity while solving PDE

I have to solve a PDE (in the context of the functional renormalization group in physics). I have a function of two variables, $U(l,p)$. I know $U(0,p)=U_0(p)$ and then I have an equation (eq925) that ...
2
votes
1answer
98 views

Funny behavior when computing dot product of coefficients with high-order polynomials

I have a similar problem to Funny behaviour when plotting a polynomial of high degree and large coefficients. However, the thing being evaluated is not just a polynomial but a dot product of some ...
2
votes
1answer
119 views

Numerical evaluation of ChebyshevT

When I evaluate the following Chebyshev series of the first kind in two different ways, I get two very different results: ...
2
votes
1answer
722 views

Numerical Integration with Variable Parameters

So I want to numerically compute the integral of a long complicated expression over a specified domain (in this case an ellipse). I know how to use a Boole function to sample within the ellipse, but I ...
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: ...
2
votes
1answer
166 views

Strange behavior when replacing variables by numerical values [duplicate]

I have a rather complicated function with parameters {a, b, c, d, e, f, k}, and I'd like to know its behavior as a function of k alone given other parameters, so I try the following code: ...
2
votes
1answer
818 views

Tutorial for basic numerical methods for PDEs

I'm afraid this is probably not going to be a "good" question, but I'd like to use Mathematica to learn about basic numerical schemes for solving pdes. For example, I'd like to compute the solution of ...
2
votes
1answer
2k 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 ...
2
votes
1answer
568 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
110 views

Mathematica Precisions vs Doubles in C/C++

I'm having a bit of an issue regarding numerical precision and I'm not sure how to deal with it. I have a certain randomly generated matrix, say $M$, that I wish to compute the eigenvalues. The ...
2
votes
1answer
105 views

Is there a good way to check, whether a small value produced numerically is a symbolic zero?

I have a complicated 4x4 matrix and need to know the eigenvalues. I expect a zero eigenvalue for physical reasons. Giving numerical values first gives me an eigenvalue of $\mathcal O(10^{-15})$. Now ...
2
votes
1answer
145 views

Fixed Points Problem with 2D Mapping

I have been playing with the mapping given by ...
2
votes
1answer
124 views

Finding a root of a parameterized integral

I have a function given as a parameterized definite integral: f[a_] := Integrate[BesselJ[0, x - a] BesselJ[0, x + a], {x, -∞, ∞}] I suspect it has a root near ...
2
votes
1answer
136 views

NMaximize and Accuracy

I have a problem with NMaximize which is best depicted by the following figure. The result indicates, that the solution mathematica finds seems to be smooth except a few outliers. How can I get rid of ...
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 ...
2
votes
1answer
628 views

Crank-Nicolson with NDSolve?

As far as I understand, the Crank-Nicolson method (a.k.a. trapezoidal method) can be expressed as a second order implicit Runge-Kutta method. It's Butcher tableau is: ...
2
votes
1answer
485 views

Problem with Covariance Matrix Output in NonlinearModelFit

I am running NonlinearModelFit based off of some simulated data and trying to fit to a function with more than one parameter. Eventually, I would like to fit to 5 ...
2
votes
1answer
65 views

Round off in Mathematica Built-in functions

Is there a way to avoid Mathematica to replace Built-in functions to other functions? For instance, the Hypergeometric1F1[a,b,x] function has a exponential form when its firsts parameters are ...
2
votes
0answers
54 views

Why can Mathematica compute numerical sums more efficiently when they are written as matrix operations?

Let $f(n)$ and $K(n,m)$ be functions such that the double sum, which we wish to evaluate numerically, $$ \sum_{n=1}^a \sum_{m=1}^a f(n) f(m) K(n,m) $$ exists when $a$ is some large positive number. I ...
2
votes
0answers
133 views

How to solve an equation where the unknown variable is inside the integration [closed]

I have an equation: $$ \frac{1}{g}=\int_0^{\frac{1}{\delta}\sinh \frac{1}{g}} \frac{\tanh\left(0.882\, b\,\delta\sqrt{1+z^2}\right)}{\sqrt{1+z^2}}\mathrm{d}z $$ I want to obtain the relation ...
2
votes
0answers
252 views

NDSolve fixed step problem

Working example here: Drive folder (have both files in the same directory! Notice: the line <<variables' in the file seems to throw an error for me, but ...
2
votes
0answers
71 views

Problem with plotting a function that calls FindRoot [closed]

I am having difficulties in plotting the solution of FindRoot to solve 4 variables. I defined a function and then tried tp plot it, but got an error message ...
2
votes
0answers
104 views

How do I numerically integrate over a data set that has uncertainties? [closed]

I have a 1D data set {xi, yi} with no uncertainties in xi and with uncertainties dyi in yi. The resulting discrete function is monotonic and relatively smooth and I would like to integrate the ...
2
votes
0answers
73 views

How can I use 'NIntegrate' to show the error?

I have to compute a very complicated integral, which is a 16-dimension one, so NIntegrate use Monte-Carlo. I have set Method -> "AdaptiveMonteCarlo, when I run ...
2
votes
0answers
73 views

Number recognition in Mathematica [duplicate]

Suppose that I have a number $n$ with many decimal digits of precision. What is the code to use to get Mathematica to recognize possible closed-form expressions for that number?
2
votes
0answers
116 views

How to handle infeasible points in FindRoot?

I am calling FindRoot[f[x,y],{{x,xInit,xMin,xMax},{y,yInit,yMin,yMax}}] where for some points {x,y}, ...
2
votes
0answers
73 views

Complicated output from simple Eigenvalues problem

I have code that uses Eigenvalues on matrices of various sizes. But the output of what should be a very simple problem, namely finding the eigenvalue of a 1x1 matrix, is overly complicated. ...
2
votes
0answers
317 views

Speeding up a numerical constrained quadratic optimization

I'm trying to solve a quadratic optimization problem in 35 variables, $\vec{α} = \left< α_1, \ldots, α_{35}\right>$: $$ \begin{aligned} &\operatorname*{maximize}_\vec{α}&&1.0\cdot ...
2
votes
0answers
53 views

NIntegrate/NSum with parameters [duplicate]

I'm trying to calculate a continuous integral within a discrete integral. Something similar to this (yet more complex): ...
2
votes
0answers
408 views

Adapting NDSolve to circumvent NDSolve::bdord: error for 1-D Euler Equations

I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a ...
2
votes
0answers
204 views

Why is FindRoot initial value far from the specified one?

I am trying to numerically find the root of a function that looks a bit like: 1/x - (SchurDecomposition[A[x]][[2]])[[1]], where ...
2
votes
0answers
516 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, ...
1
vote
1answer
214 views
1
vote
3answers
627 views

Making a calculation with high precision

I would like to make the following calculation: 1/Sqrt[1 - (150^2 10^(-4))/(9 10^16.)] - 1 Mathematica 8 returns 0. The result is obviously not 0, but my ...
1
vote
3answers
611 views

Setting the Accuracy of calculations

I need to optimize an expression that involves a number of trigonometric functions and Exp[]. How do I make sure that all my calculations have an accuracy of ...
1
vote
3answers
137 views

How can I use the command `Minimize` of this trigonometric function? [duplicate]

I want to find the minimum of the function $\sin^6 x + \cos^6 x$. I tried Minimize[{Sin[x]^6 + Cos[x]^6, 0 <= x <= 2 Pi}, x] I got {Cos[2 ArcTan[1 - ...
1
vote
1answer
262 views

Why is arithmetic faster for inexact arithmetic?

I have been trying to compute eigenvalues of a rather sizable matrix A, about $500 \times 500$ (but sparse). I asked Mathematica to compute ...
1
vote
2answers
105 views

Numerical integration does excessive coarse-graining?

I am trying to perform numerically the following integral $$\int_0^8\text{d}x\,\text{Re}\left[\frac{e^{-\frac{a^2}{2}-\frac{x^2}{2}} x^4 \sin (b x)\left(e^{-i c x} \text{erfc}\left(\frac{-c +i x ...
1
vote
1answer
100 views

How can I increase the precision of my computation?

How can I increase precision up to 15 digits for the results (EC, and that of FindRoot) computed below? ...
1
vote
1answer
83 views

Limited Precision calculation in Mathematica

I apologize upfront for the simple minded question, however i couldn't find an answer in either the Mathematica documentation or Stack exchange. I am trying to explore the effect of finite precision ...
1
vote
1answer
217 views

Precision while calculating Fourier transform

I'm trying to understand how precision works in Mathematica. Particularly I'm calculating discrete Fourier transform using the Fourier function and calculating it ...
1
vote
1answer
337 views

How can I use Mathematica to solve a Stefan Problem using an explicit scheme?

I would like to plot the temperature distribution for a particular case. the problem is stated in the paper, behind a paywall here, summarized as Consider a one-dimensional container of length l, ...