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

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1answer
48 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 ...
0
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0answers
56 views

Plotting Geodesics in Kerr

I'm interested in plotting the trajectories of null geodesics near a rotating black hole (given by the Kerr solution) which involves a system of first order differential equations. Some Context (not ...
2
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1answer
89 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 ...
1
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1answer
50 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: ...
1
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0answers
45 views

on convergence in optimization [on hold]

I am trying to solve a nonlinear programming problem using FindMinimum solver on Mathematica. When I execute, it is printing FindMinimum::eit: "The algorithm does not converge to the tolerance of ...
2
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2answers
132 views

A problem about function N [duplicate]

Toady,I have a problem about N,described as below: For example N[1/3, 5] (* ==> 0.33333*) and ...
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0answers
62 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: ...
0
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1answer
80 views

how to solve second order nonlinear coupled differential equations using NDSolve with hyperbolic function

i have to solve some solitons scattering through this coupled equations. i need to get two different graph, but still the graph did not come out. and also the equations quite complicated containing ...
4
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4answers
244 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 ...
0
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1answer
41 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 ...
16
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2answers
482 views

Obtain approximate Hessian using FindMinimum

According to the documentation, when FindMinimum is told to use the method "QuasiNewton" on a unconstrained problem, it uses the ...
0
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1answer
107 views

Fixed Point Math in MMA

I am working with a library that needs input in a Fixed Point notation. I’d like to figure out a way to convert the floating point results into fixed point representation. The fixed point length is ...
7
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1answer
707 views

Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
4
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1answer
144 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 + ...
0
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1answer
62 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
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1answer
70 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 ...
0
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0answers
27 views

NIntegrate Issue: Changing integration limits makes calculation time extremely long

After a long time developing some code in mathematica and finally getting it to work, I have unfortunately encountered an odd problem: When I change the limits of integration (and shift the function ...
1
vote
0answers
50 views

Solve set of non-linear equations with least-squares-fitting - constrain results?

I'm trying to solve a set of functions to determine the material properties from a set of measurement values. (To set up this method I just want to fit my model with some already calculated data). My ...
5
votes
3answers
273 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 ...
9
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3answers
2k views

How can I differentiate Numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
17
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2answers
224 views

Symbolic derivatives are being calculated numerically

Just found the following while debugging a problem. Mathematica is calculating the derivative of IntegerPart[x] in some odd way: ...
0
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1answer
122 views

Is this function convex?

How can I determine convexity of the function f = Log[ x, 1 + (x^a - 1) (x^b - 1)/(x - 1)] with the parameters $a,\,b$ belonging to the interval $(0,1)$ in ...
2
votes
1answer
121 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 ...
1
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0answers
47 views

How to find a scaling parameter in matrix inversion process by MMA?

I simply would like to find the inverse of a given matrix $A$ by the iterative method $X_{k+1}=X_k(2I-AX_k)$ using $X_0=\frac{1}{\sigma_{max}^2}A^*$. An example is as follows ...
0
votes
2answers
138 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 ...
5
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3answers
187 views

Numerical evaluation of a sum

I am trying to compute numerically NSum[(-1)^n/n^3, {n, 1, Infinity}]. Of course, using first Sum would work here, but often ...
0
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1answer
91 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
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1answer
73 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
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1answer
127 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 ...
4
votes
3answers
288 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
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2answers
126 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. ...
7
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4answers
366 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 ...
0
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0answers
43 views

Ideas for NDSolve?

I'm currently trying to find a numerical solution to a differential equation of the form: D[W[X], {X, 4}] ==(-(1/(delta + G - (G X)/L)^2) + 1/(delta + (G X)/L)^2) ...
0
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1answer
92 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 ...
11
votes
1answer
207 views

How to create internally optimized expression for computing with high WorkingPrecision?

I have large dataset and need to fit rather complicated function on it with different values of one of its parameters (this parameter must be fixed in every fit). I use the ...
0
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0answers
91 views

Mean Squared Deviation for Population Data

I've been using the Lotka-Volterra equation to estimate population sizes and need to find the MAD (mean absolute deviation), MSD (mean squared deviation) and mape (mean absolute percentage error) for ...
25
votes
2answers
926 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 ...
4
votes
1answer
111 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
63 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. ...
27
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5answers
2k views

Identifying critical points 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 ...
0
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1answer
76 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: ...
39
votes
8answers
2k views

Updating Wagon's FindAllCrossings2D[] function

Stan Wagon's Mathematica in Action (second edition; I haven't read the third edition and I'm hoping to eventually see it), demonstrates a nifty function called ...
2
votes
1answer
136 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
157 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 ...
0
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0answers
46 views

Numeric function not fully evaluating

I'm running into an issue where it seems Mathematica is not fully evaluating the output of my function h[t_]. I included the definition of phi[t_] just to demonstrate that it is a numerically defined ...
2
votes
1answer
208 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
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0answers
87 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: ...
2
votes
1answer
40 views

Results of ArgMax as a function of a parameter with InterpolatingFunctions

I would like to obtain a function and its derivatives, where the function is defined as the solution to a maximization problem. The obvious approach ...
32
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6answers
4k views

Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)

Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$. When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], Mathematica gives the ...