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

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4
votes
1answer
161 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 ...
4
votes
1answer
434 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 ...
4
votes
0answers
93 views

Synchrotron Radiation and ListDensityPlot

I'm trying to reproduce this plots: For this task i'm following this blog entry: Synchrotron radiation As you can see there, the task is to make a DensityPlot of a vector field essentially. This ...
4
votes
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 ...
3
votes
2answers
284 views
3
votes
2answers
564 views

Unexpected result of summation

I wrote a small module that gives me an incorrect output-set. It should be a single number! I don't understand what went wrong. This is the form of summation used: $$\frac{1}{2} (b-a) \sum_{i=1}^n ...
3
votes
2answers
249 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 ...
3
votes
3answers
799 views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
3
votes
1answer
401 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. ...
3
votes
2answers
259 views

Computing the minimum distance in a contour plot

I have the following Mathematica code ...
3
votes
3answers
277 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 ...
3
votes
3answers
144 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 ...
3
votes
1answer
387 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, ...
3
votes
2answers
465 views

Speed of convergence for NIntegrate

I'm trying to optimise numerically a function that entails computing the expected value of a truncated trivariate normal distribution and this is taking extremely long -I also get warned about ...
3
votes
1answer
86 views

Why is the Spherical Bessel Function acting strangely at this point?

I'm doing some computation that requires the use of Spherical Bessel Functions of the 1st kind, at high orders and values. So, I managed to find this, while running it over a wide range of values. I ...
3
votes
2answers
288 views

NMinimize/NMaximize is unable to generate initial points

Mathematica 10 generates a warning that it is unable to generate initial points for numerical optimization problems. I picked a particularly simple example. The problem goes away when ...
3
votes
2answers
179 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 ...
3
votes
1answer
118 views

obtaining real roots of negative numbers in a long expression [duplicate]

I have a complicated symbolic expression which contains many terms like $(a/(a-2))^{1/m}$, where $a/(a-2)$ could be positive or negative after replacement. I only need the real root after ...
3
votes
1answer
101 views

compute the gradient in high dimension

The following code is used to compute the gradient of a given 2D data. ...
3
votes
1answer
196 views

Fixed-Point Numbers in Mathematica

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 ...
3
votes
4answers
1k views

Implementing Newton's method

I have this question on coding Newton's method in Mathematica. I have some code to go by but I have no clue if it's computing the functions in the right order. The book is the numerical methods ...
3
votes
2answers
111 views

How to prevent Round with hided fractions

I found a strange behavior in Round. If we try: ToString[Round[4.811, 0.01], InputForm] we get: 4.8100000000000005 When I expected 4.81 In order to ...
3
votes
1answer
125 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: ...
3
votes
2answers
180 views

Solve-ing with initially unassigned parameters and Solve-ing using their numerical values produces different results

I am trying to solve an equation using the following piece of code: ...
3
votes
1answer
463 views

Animated Wave Propagation using Fourier & InverseFourier

This is a continuation off of previous help on the first part of my project: fourier issue arising from input miscommunication Now I want to go one step further in the current code. Here's the code ...
3
votes
1answer
806 views

Monitoring the Evaluation of NDSolve: time to finish estimation

My problem is quite simple: I run a NDSolve with a system of many ODEs, a calculation that will run for many hours, and I would like to know the progress of the ...
3
votes
1answer
257 views

Numerical Error with Large Matrices

I am writing a Finite Element Analysis program in Mathematica. The code involves handling a large matrix with large entries. I get an error when I try to use Mathematica's "LinearSolve" to solve a ...
3
votes
1answer
268 views

Strange behaviour of PolyLog Function

I discovered some strange behaviour of the PolyLog[] Function in Mathematica which seems to me like a bug in the function implementation. It looks like ...
3
votes
2answers
317 views

Numerically finding a derivative jump of a function

How would I numerically find where a function has derivative jumps? In particular, I'm working with this function: ...
3
votes
1answer
107 views

Define and refine mesh around a hole

I am solving Laplace equation with particular geometry and boundary conditions: ...
3
votes
1answer
193 views

Find the NullSpace of a matrix whose determinant is “almost” zero

If $A$ is a matrix such that $\det(A)=0$, it is easy to get a basis of the kernel of $A$ with NullSpace[A]. Now let's consider a matrix $B$, function of a ...
3
votes
1answer
79 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 ...
3
votes
1answer
1k views

Plot FindRoot for non-trivial function

I would like to plot the results of FindRoot over certain range of inputs. I tried to do this with the code: ...
3
votes
2answers
952 views

Numerically Solving two dependent Transcendental Equations

I need to solve a system similar to the following (Except it is quite large. Solving this ought to do the job): $$ \tan[2f(t)] = 1+ t^2\ $$ and $ f(t) $ is $ k $, such that$$ \tan[2kt]-(1+k^2) = 0\ ...
3
votes
2answers
68 views

Slow application of `Outer` on a matrix

I have some performance issue with the calculation of a gaussian kernel applied to a not-that-large dataset. I'm not very good with performance tuning in Mma and I have the feeling this one could be ...
3
votes
1answer
41 views

How shortening argument test when declaring functions?

When defining some functions which depend in many arguments sometimes we need to include question Q constraints to diminish processing time. My question is simple, there is a way to shorten a long ...
3
votes
1answer
73 views

Leave out a term when summing

I'm calculating the Madelung constant $$\alpha = -\sum_{n_1,n_2,n_3}{\frac{(-1)^{n_1+n_2+n_3}}{(n_1^2+n_2^2+n_3^2)^{1/2}}}$$ Where $n_1,n_2,n_3$ are any element in the integer domain and they can't ...
3
votes
1answer
585 views

Numerical solution of Bessel-like equation using NDSolve

I need to calculate solution of Bessel-like equation having general form: $\frac{d^2F}{dr^2}+\frac{1}{r}\frac{dF}{dr}+Q(r)F(r)=0$. Problems come from the points near $r=0$ leading to numeric errors. ...
3
votes
1answer
764 views

NDSolve for a large system of simple ODEs

I am solving a system of many (more than 100) ODEs. It is the kind of standard rate equation encountered in semiconductor physics. Here is the system: ...
3
votes
1answer
130 views

Find point at which equation stops having roots (if it exists)

I am interested in the roots of this function: f[M_, b_] := 1 - (2 M Gamma[2, 0, (1/M + b M)/Sqrt[b]])/(1/M + b M) for fixed values of b. In particular I want ...
3
votes
2answers
110 views

Finding solutions at non-differentiable points of a numerical function

Let's consider a 2D function we can evaluate numerically, but which is opaque to symbolic manipulation (this is just an example): ...
3
votes
1answer
295 views

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

I would like to plot fractional functions. Say $f=(\sin)^{1/2}(x)$. By that I mean that $f(f(x)) = \sin(x)$. Similarly I can define a half-derivative to be an operator such that $H[H[f(x)]] = ...
3
votes
1answer
1k views

NDSolve does not respond

For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
3
votes
1answer
40 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. ...
3
votes
1answer
85 views

Why is left NumberPadding always applied in NumberForm?

I would like to display numbers like 9.0001 and 10.0001 in the fixed-width form of xx.xxxx. ...
3
votes
1answer
199 views

Construct DifferentialMatrices and Kernel for LevinRule for this integral and ODE set

I've made a lot of progress on my problem the last few days thanks to all the help I've received on here. I think I'm upto the final step of greatly improving the performance of NIntegrate[..] on my ...
3
votes
0answers
37 views

Nonuniform Savitzky-Golay filter for smoothing and differentiation

The classical Savitzky-Golay filter works only with uniformly sampled data and currently we have at least two good implementations of it for Mathematica published on our site. But in many practical ...
3
votes
0answers
70 views

Stability analysis of transcendental equation (stability crossing curves)

I am working with a non-linear delay system with three scalar delays. After taking the Laplace transform of the linearized system, the characteristic function is a transcendental equation with three ...
3
votes
1answer
87 views

Imaginary terms in the derivative of Jacobi theta function (2) on the real line

I am trying to calculate/plot the derivative of the second Jacobi theta function $d\theta_2(0, e^{-\pi t} )/dt$. Calculating or plotting the function itself works fine: ...
3
votes
0answers
145 views

Numerical integration: complicated 2D integral seems to be poorly estimated

In the course of some physics research I've been working on, a very annoying integral has appeared that I'm having difficulty evaluating numerically. Any help you could offer would be greatly ...