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

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0
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0answers
18 views

How to get rid of numerical scope error? [duplicate]

I am trying to perform a numerical maximization routine on a setdelayed function which involves a numerical integral and I'm getting an error message. The evaluation continues and gives the right ...
9
votes
2answers
677 views

Problem with numerical evaluation of analytically solved integral, solution way off

The following command in Version 9.0.1: N[Integrate[x^50*Sin[x], {x, 0, 1}]] gives $1.4615\times 10^{48}$ which is way off from the correct solution which is ...
20
votes
7answers
618 views

Elegant high precision `log1p`?

Sometimes it is hard to understand how numerical expressions are evaluated. I remember reading claims by Wolfram on how smart the Kernel is to evaluate expressions trees numerically by recognizing ...
2
votes
1answer
114 views

Unexpected Weierstrass $\wp$-Function Behavior

In Mathematica, the Weierstrass $\wp$-function is expressed by WeierstrassP[u + I v, {g₂, g₃}] where g₂ and ...
1
vote
0answers
45 views

Numerical Derivative after numerical integration [closed]

I am trying to find the numerical derivative of a function whose argument defines the bounds of a numerical integral. ...
0
votes
1answer
71 views

Find all degenerate eigenvalues of a cubic equation

I have an equation that is cubic in w. The three solutions correspond to bands in a bandstructure, and are a function of wavevector ...
5
votes
3answers
191 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. ...
6
votes
2answers
171 views

Round vs. Floor vs. Ceiling for non-integers non-orders-of-magnitude

I understand that Round give the nearest even integer for cases where the number is between two integers, i.e. Round[2.5] = 2 ...
5
votes
2answers
398 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 ...
3
votes
1answer
128 views

Strange NSum behavior

If I do: NSum[(i + 1)/(i + 2) LegendreP[i, 0] LegendreP[i, 0], {i, 0, Infinity}] I get: 1.25216 If I do: ...
5
votes
1answer
550 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 ...
0
votes
0answers
40 views

Signage of eigenvector [duplicate]

I am comparing eigenvectors generated from mathematica to matllab. It seems signage of eigenvector generated from Mathematica is opposite from what is generated from matlab. Can anybody review and ...
1
vote
0answers
63 views

Floor inconsistent with Less for machine-precision approximate numbers

For machine-precision numbers, Mathematica uses a tolerance for comparisons, so that 1.-$MachineEpsilon==1. However, Floor does ...
1
vote
0answers
28 views

Function to be used for spectral decompostion of matrix [duplicate]

Can anybody please help in finding out what is best way to do spectral decomposition (or Eigen decomposition) of the matrix. The details of Eigen decomposition can be found in attached link 1. ...
1
vote
0answers
54 views

Union sorting after ignoring some digits

I have a list with its bellow elements: {-0.7071067811865476, -0.7071067811865475, 0.7071067811865475, 0.7071067811865476} If I use Union, but there is no change. Because the numbers are different. ...
4
votes
2answers
116 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: ...
19
votes
1answer
337 views

Faster binary Hamming weight for big integers?

While working on an answer to Count the sequences in an array I found that DigitCount was the bottleneck in my code when used as ...
4
votes
1answer
248 views

Numerical errors/inaccuracies in ProductLog

Context In cosmology, a fairly accurate model to describe the gravitational potential, $\psi(r)$ of dark matter halos is given by $\psi( r)=\log(1+r)/r$. ...
1
vote
0answers
59 views

Improve speed of evaluating a sum over four indices

I am trying to implement the Fox-H function with several variables as sum of residues. I have arrived at the following function; ...
10
votes
4answers
1k views

Function to subdivide interval into n evenly-spaced points

[This post needs better tags than I could come up with. Edits to the tags would be particularly welcome.] I realize that it is trivial to define a function that takes an interval (i.e. two ...
0
votes
1answer
48 views

NDsolve with discontinuous non-numeric PDE coefficients

I want to solve the heat diffusion equation with variable thermal conductivity. So I have the following code ...
1
vote
1answer
38 views

Generation of list of values for small gap among values

I need to run a loop as Table[expr,{i,imin,imax,di}] where I want di to be as small as order of ...
9
votes
2answers
96 views
1
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0answers
194 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 ...
0
votes
0answers
23 views

Why does `NSolve` not solve this system of equations on a bounded domain?

I have three functions $E1,E2,E3$ of $t1$ and $t2$. The expressions are slightly complicated and involve trigonometric functions. For clarity purpose, they are given at the end of the question. I ...
5
votes
1answer
63 views

Can Someone Please Explain Internal`$SameQTolerance?

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

Steady State Numerical Solution of Heat Diffusion Equation in 2D

I'v been trying to solve for the steady state of the heat diffusion equation numerically but I cant seem to get it to work. My code is ...
3
votes
1answer
210 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 ...
2
votes
0answers
54 views

Problem with plotting a function that calls FindRoot

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 ...
0
votes
1answer
431 views

Trying to solve a transcendental equation involving Bessel functions

I've never used Mathematica before and am trying to numerically solve equation (12) from this paper. Ideally I'd be able to find the smallest value of $x_{n\nu}$ for $\exp(-kr\pi)$ close to 1, and ...
0
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0answers
34 views

Why is there a different eigenvector for the same matrix? [duplicate]

I have a matrix that depends on two variables x and y. Matrix[x,y] When I make x=-.25*(1 - 1/3) + .25*(1/3) + .25 y=0 I ...
31
votes
3answers
4k views

Understanding differences between Maple and Mathematica in examples picked by Maplesoft

I am reading the document How Maple Compares to Mathematica. On page 15 there is an example where Mathematica produces wrong results. Does anybody know why? MAPLE: MATHEMATICA: Also on page 17 ...
8
votes
2answers
702 views

Finding differences between Pi with varying number of decimals

I have the following code In[32]:= N[Pi, 2] Out[32]= 3.1 In[33]:= N[Pi, 1] Out[33]= 3. In[34]:= N[Pi, 2] - N[Pi, 1] Out[34]= 0.*10^-1 Why can't Mathematica ...
16
votes
2answers
294 views

How to improve performance of BesselJ to the level of GSL?

Consider the following code: zs = N /@ Range[0, 12, 10^-5]; AbsoluteTiming[bessels = BesselJ[1, #] & /@ zs;] Length@zs I've tried to measure only computation ...
0
votes
0answers
17 views

Increasing the zero threshold [duplicate]

I have a function similar to this: func[x_]:=Log[1+x] when I evaluate it at very small arguments, it will become 0, i.e. ...
9
votes
5answers
311 views

Function for a series of joined slopes

I need a function for a series of joined slopes and my solution feels a bit kludgy. Is there a better way? A list of pairs of transition points and slopes: ...
13
votes
1answer
421 views

Why is MainEvaluate being used when LinearSolve can be compiled?

According to this question LinearSolve can be compiled. However, CompilePrint[] shows a call to ...
0
votes
1answer
42 views

Is there a package that can calculate the Ricci tensor from a numerically given metric?

There are many packages about general relativity or differential geometry, and they can calculate the Ricci tensor from a symbolically given metric, for example, $g_{tt}=-f(r)$, $g_{rr}=h(r)$, etc. ...
3
votes
0answers
60 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
90 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
2answers
121 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 ...
2
votes
2answers
97 views

Calculate area between two multivalued curves

I have to calculate the area between two curves which will give me the result of a particular quantity. However, both the curves are multivalued functions. Here is a data set showing the region where ...
3
votes
2answers
261 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 ...
0
votes
0answers
69 views

Solving a Transcendental Function of two variables numerically

I have a transcendental function F of two variables, i.e. F(x,y). The function F contains ...
1
vote
1answer
134 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
45 views

Multiplying two parametric solutions

I'm solving two (1-parameter) differential equations and I want to plot the product of their solutions, how do I do this? Here's the code, ...
7
votes
3answers
475 views

Implement the Bisection algorithm elegantly and easily

Description: Rencently, I have finished my course Numerical Analysis, so I'd like to implement many algorithm that I have learned from that course.By this practice, I hope that I can improve my ...