Questions tagged [numerics]
Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.
-3
votes
0answers
50 views
How to design and deal with repeating decimals? [on hold]
Repeating decimals could be represented by fractions.
Given
$
\huge{\frac{1}{3}=0.33333\overset{!}{3}}\tag{1}
$
if multiply $3$ on both sides,is this step wrong?...
3
votes
2answers
141 views
1
vote
2answers
103 views
Multivariate Newton-Raphson method and FindRoot module [on hold]
Let's suppose that we have the following equation
...
5
votes
2answers
135 views
Does Mathematica gives us a wrong result for the integral of a function including elliptic functions?
Calculus tells us that the differentiation of the integral of a function should be itself, but at least in one case Mathematica answers NO. I feel very confused. The new figure seems to bifurcate at ...
3
votes
1answer
84 views
Problem with the Inverse CDF of Non-central F Ratio Distribution
In[3]:= n = 5; n1 = 4; n2 = 6; γ = 0.05; α = 1/370;
InverseCDF[NoncentralFRatioDistribution[1, n1 - 1, n1/γ^2],
1 - α - (n - n1)/n2]
During evaluation of In[3]...
0
votes
0answers
34 views
Numerical solution to approximate the singular integration using collocation method
I am working to solve "numerically" the following integral equation IE:
u[x]=f[x]+Integrate[(1/(x-t)^(1/4))*u[t],{t,0,x}]+Integrate[(1/(x-t)^(1/4))*u[t],{t,0,1}]
...
5
votes
1answer
113 views
Recycling solutions of multidimensional NDSolve
Dear wolfram community,
I hope my problem is clear and easy to solve.
I have already solved the following heat equation over a domain:
...
0
votes
1answer
96 views
Problems with numerical integration
I tried to plot beam intensity using a function that evaluates a numerical integral, but it didn't work.
Here is my code, which did not produce a result.
...
4
votes
1answer
77 views
Catastrophic loss of accuracy in Orthogonalize
Context
In connection to this question
I am interested in orthogonalizing known matrices.
As a test case, let us consider the definite positive 15 x 15 matrix mat
...
0
votes
1answer
51 views
Good practice about numerical precision
In one of my calculations, I get -1.11022*10^-16 as one of my eigenvalues for a matrix. It's essentially zero and I suppose I could use SetPrecision to make it zero but I wonder what's a good practice ...
0
votes
1answer
53 views
Increasing MaxExtraPrecision arbitrarily changes numerical result
I am trying to confirm that a function $f$ satisfies a particular differential equation of the type $D f=0$, for some differential operator $D$. I set $Df$ as Diffeq...
4
votes
3answers
259 views
Turn the following values into percentage [closed]
I have the following data:
{2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017}
{5914, 6143, 6182, 18000, 18173, 18344, 18454, 18506, 18800, 19216}
My data is already in Matrix form in ...
0
votes
0answers
39 views
High numerical precision failing [duplicate]
N[(1 - 2*6.674*6*10^13/(6371000*299792458^2))^(0.5), 20]
1.
What I expect:
...
1
vote
2answers
158 views
A numerical boundary conditions paradox
For $(t,z)\in[0,1]\times[-1,0]$
zmin = -1; tmax = 1;
and some fields $w(t,z)$ and $y(t,z)$
...
1
vote
1answer
29 views
NIntegrate fails with functions that have (necessarily) numeric lists as arguments
I'm not able to NIntegrate a function that has a numeric list as an argument. My original problem involves a compiled function, but a MWE is the following:
...
6
votes
1answer
123 views
Looking for examples of numerically solving coupled PDE and ODE
I am about to solve a system of coupled PDE and ODE in thermodynamics. My system is a bit complicated, so I would like to learn from some examples before coding my own system.
I searched this site ...
0
votes
1answer
50 views
Wrong divergence with numerical value
this is my first question in this forum.
I'm trying to evaluate some complicated function of, say, $x$ near $x=0$ (in order to integrate it later). The problem is that the numerical value of this ...
0
votes
1answer
88 views
Removing zero dot after solving
I've a question regarding "zero dots". Im using a lot of calculation in an application which i am building within mathematica. However when i use the output of solve for instant i will not have the ...
2
votes
4answers
146 views
How to generate repetitive graphs?
I need to create several graph for different values of a parameter $h$.
The code is the following
...
0
votes
1answer
36 views
numerical integration with intermediate variables
I'm trying to perform the following integral, where the bounds of the inner integrals become the integration variable in the next integral.
disregarding the stuff in the exponential in the sample ...
4
votes
1answer
227 views
Dynamic, nonlinear, damped Euler–Bernoulli beam equation
I would like to solve the 3 coupled PDEs describing a damped, nonlinear (i.e displacements in the $x$ direction along the beam need to be considered along with the $y$ displacements normally ...
0
votes
1answer
31 views
PDE's numerical integration: simplify output: get rid of $[t,r]$'s and ${}^{(0,1)}$'s
When numerically integrating PDE's systems mathematica output can be chaotic and therfore time-consuming or even impossible to understand and use.
A major source of confusion are the $[t,r]$'s and ${...
0
votes
0answers
15 views
NDSolve: Method of Lines: same grids for spatial discretization: error: stiff system_zero step size
How can I modify bbgofrey's answer so as to use $n+1$ grid points for variable $y$? My code
...
1
vote
1answer
58 views
Non Trivial Conserved Quantity Fails To Be Conserved After Solving System of ODE's Via NDSolve
I'm trying to solve the following Darboux system of equations numerically.
As a result I have the following implementation of NDSolve
...
1
vote
2answers
51 views
Numerics & List Manipulation:ListCorrelate: yield $\{-f1 + f2, \dots, -f2 + f4, \dots\}$ from $\{f1, f2, f3, f4, f5\}$
The command
ListCorrelate[{-1, 1}, {f1, f2, f3, f4, f5}]
yields
{-f1 + f2, -f2 + f3, -f3 + f4, -f4 + f5}
is there any simple way to get
{-f1 + f2, -f1 + ...
0
votes
1answer
41 views
Why does trying to plot the solution to this system of ODEs this way lead to errors?
I would like to plot the curve $\alpha(s) = (l(s), h(s))$, where $l$ and $h$ are the solutions to the system $l'^2 + h'^2 = 1$ and $l'h''-l''h'=h'\tan(l)$. Here's what I tried:
...
3
votes
1answer
141 views
Eigenvalues of a non-Hermitian complex periodic potential
I have an eigenvalue problem:
$$-\frac{d^2}{dx^2} \psi(x) +V(x)\psi(x) = E \psi(x)$$
where $V(x)$ is a complex periodic potential:
$$V(x) = 4[\cos^2(x) + i 0.3 \sin(2x)]$$
It has been claimed that ...
1
vote
1answer
31 views
Find a matrix $X$ that block-diagonalizes a particular group of matrices
Essentially, I want to find a single matrix $X$ such that conjugation by $X$ sends:
$$\begin{bmatrix}
1 & 0 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 & 0 \\
0 & 0 & 1 &...
1
vote
2answers
72 views
how can I make a grid? [closed]
I would like to make a grid for x between 0 to 1
and use following Table
...
0
votes
1answer
110 views
Why can”t I get a smooth curve?
I used "Table" to calculate and plot the following complicated function. First, we choose an initial value for $G$ and other parameters, but at later times $G$ changes with function $I_a$.
...
3
votes
0answers
42 views
ContinuedFraction: different result with different representation of argument
Why if I write:
In[7]:= ContinuedFraction[3.15]
FromContinuedFraction[%]
N[%]
I get:
...
1
vote
1answer
41 views
Performing a FindRoot from Numerical integration
I am trying to evaluate:
FindRoot[Xfnew[γ, w, Hi, mx]*92*10^23*γ^(4/(1 + w)) == 1198/10000, {Hi, hs},
MaxIterations -> 10000]
for some starting value hs,...
2
votes
1answer
52 views
ParallelDo gives different solution to Eigensystem
I am trying to calculate the eigensystem of a large matrix (e.g. 256x256). I have found that when I do this within a ParallelDo (because I am actually calculating many of these eigensystems), the ...
2
votes
0answers
48 views
How to construct a time-dependent matrix quickly?
In the process of discretization of a 4D PDE, I need to construct a final sparse matrix $B$, which is very large (I denoted by $\text{size}$ here) and time-dependent, viz, some of its entries change ...
0
votes
0answers
22 views
Properly parallelising FindRoot for multiple starting values
I have a problem I want to find numerical solutions for with different starting variables. Let F be a vector supposed to vanish, which in its definition includes ...
0
votes
1answer
45 views
Solve nonlinear differential equation system (Plot solution)
When I solve the system of differential equations I get two solutions for each variable (See the picture). My question is how I can neglect one of the solutions at the plot (The yellow and the blue). ...
1
vote
2answers
113 views
I have two lists that are the same, yet I get a FALSE when i try to show they are equivalent
I have tried changing the variables, reevaluating the cells, but it just keeps giving me false. The weird part is that it was originally true and it changed to false, randomly.I did not want to post ...
3
votes
1answer
99 views
Solve a system of 4-th order polynomial equations (numerically)
I have a function defined on $ S^6 \times S^6 $ (two spheres embedded in $ \mathbb{R}^7 $ individually). Let us call this vector $ \vec{f}(\vec{x},\vec{y}) $, where $ \vec{x} $ and $ \vec{y} $ are ...
3
votes
1answer
45 views
Numerical precision problem
I have this simple code:
ep = 1 - 80000000000 (-(199999/200000) + 1/E^(1/200000))
ep // N
-8.27404*10^-8
...
0
votes
1answer
50 views
Finding the best representation of a numerically-inverted function via InterpolatingPolynomial and/or variations
Below is the routine I am using to sort of represent the numerically-inverted function $TP$. Basically I am finding a necessary interpolating polynomial $TPint$ that fits with the data points given by ...
1
vote
0answers
36 views
Finding zero linear combinations of polynomials (numerically)
I have two functions of real variables defined on two compact spaces
...
0
votes
1answer
46 views
Total derivative after numerical solution of a system
I have a system of three equations in three unknowns, $k$, $\theta$ and $w$. I am interested in the behavior of the variables when one parameter changes. I first specify the system:
...
0
votes
0answers
41 views
Proper implementation of numerically integrated function inside a differential equation
I have a numerically-inverted function TP which is then fed to the differential equation below. My question is: What is the right way to implement this ...
0
votes
0answers
13 views
Relationship between working precision and precision
Please is it possible that the working precision specified for a particular computation be equal to the precision of the numerical value gotten. What are the conditions that would make the numerical ...
4
votes
1answer
48 views
AccuracyGoal & PrecisionGoal: how to know which was used to yield the result?
With NMinimize (or many other functions), when an answer is found without any warnings, this means that a certain convergence criterium was achieved. It could be ...
1
vote
0answers
33 views
Do you know what's issue of my code, NDsolve and ParametricPlot [closed]
Could you please point out my isse of the code?
Frustrated.
...
8
votes
2answers
108 views
Robust DuplicateFreeQ for numerical data
I am looking for a fast and robust DuplicateFreeQ equivalent for numerical data. Floating point numbers should normally be compared with some tolerance, as ...
1
vote
1answer
42 views
Interpolation error of InterpolatingPolynomial[]
this is my first post so if I have any error while writing this, I'm sorry.
I had to do a polynomic interpolation for one of my lab experiments, and I need to get the error from it in order to ...
3
votes
1answer
83 views
Problem involving a system of nonlinear coupled ODE's with adjustable boundary
The problem is to solve the following system ODEs:
I. $\ \ \ \ \ \ \ \dfrac{4}{r}[1+a(r)]\left(\dfrac{dH}{dr}\right)^2+\dfrac{dG}{dr}=0$
II. $\ \ \ \ \dfrac{1}{r}\left(\dfrac{dA}{dr}\right)+f(r)+k^...
23
votes
1answer
288 views
Which second arguments is VectorQ/MatrixQ/ArrayQ optimized for?
VectorQ and similar functions (MatrixQ, ArrayQ) treat certain second arguments specially.
...
