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

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10
votes
4answers
2k 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
92 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
39 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
123 views
1
vote
0answers
235 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
34 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
74 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
201 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
277 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
65 views

Problem with plotting a function that calls FindRoot [closed]

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
0answers
36 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 ...
36
votes
3answers
6k 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
728 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 ...
0
votes
0answers
18 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
323 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: ...
15
votes
1answer
457 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 ...
1
vote
1answer
61 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
106 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
112 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
140 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
119 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
298 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 ...
1
vote
1answer
183 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
54 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
774 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 ...
3
votes
3answers
2k 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 ...
2
votes
1answer
115 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
4k 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
451 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 ...
8
votes
2answers
612 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 ...
1
vote
0answers
99 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 ...
15
votes
2answers
511 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, ...
1
vote
2answers
116 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). ...
5
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.)?
1
vote
1answer
86 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
150 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
202 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
215 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
56 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 $\frac{m(m-1)}{2}$ ...
0
votes
1answer
61 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
572 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
66 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
142 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 ...
3
votes
1answer
101 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 ...
11
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
72 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: ...
3
votes
0answers
251 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
125 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
268 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 ...