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

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8
votes
2answers
700 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
290 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
309 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
413 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
40 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
48 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
2answers
585 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
0answers
81 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
114 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
93 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
253 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
60 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
122 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
44 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
451 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 ...
17
votes
1answer
687 views

Dual complex integral over implicit path using contour plot

Context I am interested in doing double contour integral over paths which are defined implicitely. For the sake of debugging, let's assume its $$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
3
votes
3answers
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 ...
4
votes
0answers
97 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 ...
2
votes
1answer
105 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: ...
20
votes
2answers
3k views

How to fit 3 data sets to a model of 4 differential equations?

I'm a biologist and a newbie in Mathematica. I want to fit three data sets to a model consisting of four differential equations and 10 parameters. I want to find the parameters best fitting to my ...
6
votes
2answers
314 views

A problem about fixed point iteration theory

Description Recently, I have been learning a couse called "Numerical Analysis". The fixed point iteration theory was introducted to solve the ...
9
votes
1answer
166 views

Does Mathematica have an equivalent of C's nextafter?

In C (and many other programming languages), there is a function double nextafter(double x, double y) which takes two (IEEE 754) floating-point numbers and ...
8
votes
2answers
554 views

Is there any fast way to solve a quadratic matrix equation in Mathematica approximately?

Let the square nonsingular matrix $M$ is a given convergent matrix. What are the best scalar values for $\alpha$ and $\beta$ (in the real numbers domain), at which the following quadratic matrix ...
3
votes
0answers
131 views

Mod[1.2, 0.2] is not equal to zero

I'm new to mathematica but this doesn't seem to make any sence In[1]:=Mod[1.2, 0.2] Out[1]=0.2 Why is it not zero? Edit: This is what I wanted to do: ...
1
vote
0answers
80 views

How to incorporate the boundary conditions into the differentiation scheme in MMA?

Let that we want to numerically solve the following PDE \begin{equation}\label{sde} -r V(S,t)+r S \frac{\partial V(S,t)}{\partial S}+0.5 S^2 \text{sigma}^2 \frac{\partial ^2V(S,t)}{\partial ...
14
votes
2answers
451 views

Determining the default Method used in optimization and root-finding algorithms

Is it possible to extract the Method which is used in functions like NMinimize, FindRoot, ...
0
votes
0answers
46 views
1
vote
2answers
88 views

Plot ParametricNDSolve

I am trying to plot the probability of a molecule being in a certain state via the numerical solution of the Schrödinger's equation of molecule in an oscillating electric field (in a rotating system). ...
4
votes
4answers
2k views

Numerical differentiation methods

Is it possible to write code in Mathematica that implements various differentiation methods (like forward, central, extrapolated, etc.)?
0
votes
0answers
49 views

Solve an integral equation: to fit the given data with an integral of two functions?

I am trying to find an efficient way to solve the following equation $$h\left(b\right)=\int_{0}^{b}f\left(\frac{b-c}{1-c}\right)\frac{g\left(c\right)}{1-c}dc$$ where for $h(b)$ I have the data ...
1
vote
1answer
82 views

Is it possible to solve a certain set of nonlinear equations in Mathematica?

I read this question in a Chinese forum last year. At the end of the discussion, they provide a solution of the equations from a C++ program. Unfortunately, they did not get the right answer. ...
2
votes
1answer
126 views

NIntegrate Warning / Error Messages

I am doing: NIntegrate[Sin[Exp[(x^4)]], {x, 2, Infinity}, PrecisionGoal -> 12] It prints out a host of warnings, but also shows the results as: ...
6
votes
1answer
173 views

Numerical error in Mathieu functions

Consider the MathieuCharacteristicA function, which is a piecewise function according to the documentation. The discontinuity happens at integer number. ...
16
votes
0answers
197 views

Is MathieuC for moderately large imaginary arguments broken?

I'm trying to plot MathieuC[-3,0.3,I x] for $x\in[0,10]$, and here's what I get even with arbitrary precision arithmetic (here I use ...
0
votes
0answers
43 views

Finding common roots to several functions

I am trying to solve the following problem. Given $a\in\mathbb R^n$, $u\in\mathbb{R}^n$, $m\in\mathbb{N}^\star$, Find the/some common roots $(t_1,...,t_m)$ of the $\frac{m(m-1)}{2}$ ...
49
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 ...
0
votes
1answer
54 views

NDSolve::bcsol?

I'm writing a code to numerically solve a differential equation. It has to repeat the process several times since there is a variable involved which is unknown, and the equation is fit to some ...
18
votes
2answers
504 views

Different floating-point numbers equal?

Let's define two different numbers. x = 1. y = 1. + 2^-52 (* equivalently, 1 + $MachineEpsilon *) Let's make sure they're different with ...
0
votes
1answer
62 views

Problem with Erf near Infinity in NSolve

I have to solve a differential equation involving the error function Erf, but my code is not able to evaluate it in the range I need. I think I can formulate my ...
1
vote
1answer
138 views

Why does it matter at what point I replace?

I need to find four orthogonal linear combinations of complicated functions, that vanish at four different points. I use (LK4 is defined below, but its shape should have nothing to do with my ...
0
votes
0answers
57 views

BVP Non Linear Shooting Method Implementation

I've been working on this problem for several days. I want to split a 2nd order ode bvp into two auxillary ivps and use those to approximate the solution to the bvp. I have managed to get one ...
3
votes
1answer
87 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 ...
10
votes
3answers
4k views

Does Mathematica get Pi wrong?

I happened to watch a Youtube video on Pi. According to the video, the 1 millionth digit of Pi is 1. And here is another page of the first 1 million digits of Pi. You can get the same answer from ...
6
votes
0answers
62 views

Negative accuracy numerics ( 0``-128 notation )

What does it mean to have a negative accuracy number? I understand 0``128 to mean "the number zero to 128 decimal points". Mathematica corroborates this: ...
2
votes
0answers
121 views

Problem solving a nonlinear partial differential diffusion equation [closed]

EDIT: actualy the nonlinear partial differential equations for interacting density distributions, including boundary conditions, should be given as $$ \frac{\partial\phi}{\partial t} = D ...
5
votes
2answers
114 views

A problem with Compile and Map

There is a weird behavior of Compile that I do not understand. Consider the following example: ...
2
votes
2answers
162 views

NIntegrate over a list of functions

This question is the result of these other two questions. Question 1 and 2. I thought it would be better to ask a new question rather than deleting previous one. I think When ...
3
votes
1answer
482 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 ...
0
votes
1answer
67 views

usage of random numbers in recursive loop

I am trying to evalute two functions using iterative process as below ...