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

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7
votes
1answer
269 views

Fractal dimension of a large networked molecular system

I am trying to determine the fractal dimension of this complex biomolecule (figure attached). Any clues as to how this can be done. In trying to determine this quantity, I wonder how its ...
1
vote
1answer
126 views

Applying N to the roots found by Solve gives complex numbers when the roots are real [closed]

I have a function which is f(x) = x^3 - 5 x^2 - x + 1. When I solve for x to find the zeros ...
3
votes
2answers
202 views

Rounding the coeffcients in a polynomial

I have a very large polynomial with Complex Numbers as coefficients. Due to many calculations, there are rounding off errors. I know however by theoretical considerations, that the coefficients are ...
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 ...
2
votes
2answers
330 views

How do I feed data points into an equation to solve NUMERICALLY?

I start with this equation and solve it numerically for $z(x,y)$ in the range $1 < x < 5$ and $1 < y < 5$: $$ \frac{3}{xyz} - 2x - 3y - 5z = 0 $$ Then using the data points of $z$ above, ...
2
votes
1answer
247 views

NDSolve fails for certain choices of parameters and solve range

I'm trying to solve a pair of coupled ODEs with NDSolve. I know roughly what the solution should look like (both should give periodic functions, pi/2 out of phase, the amplitude of which damp towards ...
11
votes
2answers
644 views

FEM: Nicer Element Shape for Spherical Region

I'm trying to generate a mesh for later use in the Finite Element Method of the DSolve command. It is basically a parallelepiped with a spherical indentation. I'm ...
4
votes
1answer
100 views

How to implement something like NMaximize[ NMinimize [ f(x,y) , {x} ], {y} ]?

Title says it all, really. I want to find some set of values for which a function of those values can't be made larger than a certain number, when some other values (on which that function is also ...
2
votes
1answer
760 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
128 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 <...
3
votes
3answers
191 views

Solving determinant of a Kronecker product of matrices gives a numerical error - why?

I am doing the following steps (code at the end of the post): I start with a 2x2 matrix (smatrix), which is a function of a single variable (u2). I want to set the determinant of this matrix (...
4
votes
1answer
138 views

Bad numerical approximations

I'm trying to do some calculations here, but for some reason Mathematica starts using numerical approximations that are no good for my work. Specifically: ...
6
votes
3answers
617 views

Numerically integrating a list-valued function [duplicate]

I want to NIntegrate a List valued function foo[x] which is only defined for numerical ...
2
votes
1answer
243 views

How can I reduce computation time while still obtaining a good approximation for my function?

I am new to any CAS (and Mathematica, for that matter) and new to StackExchange too, so forgive me and correct me on any mistakes. I have this function: $J_p=\sum_{m,n=1}^{\infty} \epsilon_{mn}f_{mn}\...
1
vote
1answer
100 views

Whats the most efficient way to solve an equation numericaly (because it has no analitical solution)

So, I think the problem that Im having is simple but, still, Im not sure on how to do it. I have an equation with no analitical solution: $a_1 \sin \left(2 \theta \right)+a_2 \sin \left(2 \phi\right)...
8
votes
4answers
584 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 ...
2
votes
0answers
119 views

How to handle infeasible points in FindRoot? [on hold]

I am calling FindRoot[f[x,y],{{x,xInit,xMin,xMax},{y,yInit,yMin,yMax}}] where for some points {x,y}, ...
1
vote
1answer
92 views

How to solve the warning problem and obtain real roots without imaginary part?

I am trying to solve a equation with Newton's method via FindRoot, and the codes are: Define the functions: ...
18
votes
1answer
412 views

How can I mend this broken heart?

Try to evaluate the following code: ...
1
vote
1answer
203 views

Mathematica unable to solve equation numerically while Wolfram|Alpha can

I want to solve the following equation 2 x == Sinh[x] Mathematica is unable to do so ...
0
votes
0answers
169 views

NMinimize gives an obvious wrong value

I'm trying to minimize a function of 2 lists of the same lenght, but for now the first list has one element, the second is constant. Essentialy, this baffles me: ...
4
votes
4answers
292 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 ...
1
vote
1answer
79 views

How to make a discretized NMinimize more precise

I am using Mathematica for physics research and I want to minimize a Hamiltonian equation with respect to two variables (I have also discretized the problem). I have a single constraint. When I plot ...
8
votes
1answer
1k views

Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
4
votes
1answer
725 views

Using NDSolve to solve Equation of Motion in cylindrical coordinates

I have a set of coupled differential equations which represents the equation of motion of a particle in cylindrical coordinates with the following Hamiltonian: $$ H=\frac{1}{2m} \left( p_r^2 + \frac{...
0
votes
1answer
124 views

Find exact value

I want to know exact x'[t] value where z[t]=0 I know approximate x'[t] value is 107 but I cannot find how to find exact x'[t] value ...
1
vote
1answer
369 views

FindRoot with vector functions

I'm trying to solve a system of non-linear equations with FindRoot, and I get the answer, but also a ...
6
votes
3answers
629 views

RK4 Gravity Simulator

I have the following RK4 solver which splits the two 2nd order ODEs, used to calculate x and y positions under the influence of a gravitating body where $$x''(t)=\frac{G m x(t)}{(x(t)^2+y(t)^2)^{3/2}}$...
2
votes
1answer
417 views

Euler's method for a 2nd order ODE

This is my first post on this site. Also, I'm new to Mathematica. I'm trying to solve my first problem with Mathematica. It's about solving a 2nd order differential equation. I dont have the explicit ...
0
votes
2answers
489 views

find the real root

I have the following equation: \begin{equation} (y-1)^{b1} - C~~ y~~ \exp(a x)=0 \end{equation} where $a, b$ are real constants, $C$ may be a complex number. I need to find the real solution of the ...
0
votes
1answer
372 views

Solving for the time-evolution operator in a periodically driven system

I am looking at the Hamiltonian $$H(t)=\begin{pmatrix} 0 & e^{i\Omega t}\\ e^{-i\Omega t}& 0\end{pmatrix}$$ I am trying to solve for the unitary operator $U(t,0)=\mathcal{T}\exp(-i\int_0^t ...
0
votes
1answer
107 views

Numerical vs Symbolic Integration: Loss of precision

I am trying to integrate the following expression over the time interval $0\leq t \leq \text{period}$. ...
1
vote
1answer
1k views

Runge-Kutta 2nd Order ODE Solver

Suppose I have a 2nd order ODE of the form y''(t) = 1/y with y(0) = 0 and y'(0) = 10, and ...
8
votes
3answers
3k views

Creating a 3D List Line Plot From Discrete Points

Given the following Runge-Kutta ODE solver and the graphical output below, how do I get a 3D line plot instead of a 3D point plot? I see that there is no ListLinePlot3D function, so I thought it might ...
0
votes
2answers
380 views

Numeric mixed derivatives

In short I need NumericCalculus`ND extended to mixed partial derivatives. This can be done by nesting them, but care has to be taken to evaluate underling ND only when the parameters become numeric. ...
0
votes
1answer
98 views

How to implement the second loop

Here I have a problem that probably needs two loops, but I am not sure how to implement them together. The code calculates M for various values of parameter ...
31
votes
2answers
2k 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 ...
5
votes
1answer
199 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 ...
2
votes
0answers
74 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. ...
0
votes
1answer
385 views

NMinimize holding problem

I have a function that I want to minimize numerically through an NMinimize command (because it's very complicated analytically). The minimizer call looks as follows: ...
2
votes
1answer
416 views

Area between Contours in ContourPlot

I feel slightly foolish for asking this because I am so close, but I'm having trouble, so I will anyway. I asked this question two days ago regarding finding the lengths of contours. Now, I'd like to ...
4
votes
1answer
255 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
564 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
117 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
230 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
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 ...
1
vote
1answer
327 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): ...