Questions tagged [numerics]
Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.
1,844
questions
0
votes
0answers
73 views
Why does Mathematica store numerical values in a fresh kernel?
For some reason, when I try to do a computation in a fresh kernel, MM remembers the "old" values from the old kernel, is there a way to stop this?
1
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0answers
122 views
How to numerically solve this system?
Our system:
\begin{align}
\dot S &= \mu -\beta_1 S I_2 -\beta_2 S J-\beta_3 S A - \nu S\\[2ex]
\dot {I_1} &= p \beta_1 S I_1 +q \beta_2 S J +r \beta_3 S A + \xi_1 J- b_1 I_1 \\[2ex]
\dot{...
1
vote
0answers
142 views
+100
Optimization for numerical integration of Airy function and using NIntegrate inside NDSolve
Sorry for the long post. I need to integrate a function which uses the trajectory data given by the Lorentz force equation. We have the electromagnetic field:
$$
\vec{E}=E_0 \cos{\omega(t+\bar{z})}\...
0
votes
1answer
34 views
NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0.` [closed]
I am unable to get a numerical solution to a system of two coupled second order differential equations using NDSolve. These coupled ODEs are for a physical phenomenon known as a looping pendulum, and ...
0
votes
1answer
73 views
Two problems with ConjugateGradient
I am trying to solve a maximization problem for which I give you the code and try to step by step show you were it broke down. The first issue is that I have a constrained problem, which I try to ...
1
vote
0answers
24 views
N on equation with numbered variables [duplicate]
Say I have a system of polynomial equations in the variables x[1],...,x[n]. Sometimes want to make such equations numerical (as in: the coefficients become floats) ...
0
votes
0answers
27 views
0
votes
1answer
66 views
Solving Second Order Differential Equation with Discrete Time Data
Given the Second Order Differential Equation:
$$ m\ddot{x}+c\dot{x}+kx = \mathrm{F}_{external}^{} $$
where $ m, c, k $ are constants and $\mathrm{F}_{external}^{}$ is buffer of external force taken ...
0
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0answers
27 views
Mean error of finite differences derivative
I wrote a module that computes the 4-th order finite difference derivative of a function at $N$ equidistant points of an interval and the difference between the exact and numerical value at those ...
-1
votes
1answer
94 views
A No-linear differential equation
I'm recently figuring out how to make this equation solved but Mathematica does not solve this??!!
DSolve[{ y'[t]== ((3 a)/2 (y[t] - b/(2 a))^2 + k ((3 a)/2 - 1) t^-2 - ((a f)/2 + (3 b^2)/(8 a)))/(t ...
4
votes
3answers
163 views
How to use Findroot in a loop
Consider:
i = 0.1;
While[
i < 0.9,
y[x_] :=
y /. FindRoot[{u/(1 - u) (x + Log[y]) - 1 /. u -> i}, {y, 3}];
Plot[y[x], {x, 0, 4}];
i = i + 0.1]
I want ...
0
votes
0answers
30 views
4
votes
1answer
70 views
Using the result of NIntegrate as a potential in NDEigensysem
I am trying to find the eigenvalues and eigenstates of a Hamiltonian with a potential which cannot be analytically defined. In particular, it is the integral of the product between two functions:
<...
2
votes
1answer
60 views
Strange behavior of NDSolve (Error NDSolve::ntdvdae)
i discovered a weird behavior using ```NDSolve``` to solve a set of differential equations.
Let me outline my problem:
I need to solve a set of differential equations. These are equations of motion ...
0
votes
0answers
36 views
NMinimize too slow with non-linear constraints. Help to speed it up
First, let me introduce some parameters:
...
0
votes
0answers
55 views
A case for matrix multiplication (a.b).c unequal to a.(b.c) in mathematica 12.0.0.0, why?
The motivation of my calculation is to get the inverse for the following matrix
...
1
vote
2answers
75 views
How to Plot an Equation, based on another plot [closed]
I've been struggling with this problem That I have an equation with two variables. One of them has a defined interval. Like this:
...
0
votes
1answer
75 views
Plotting a phase plane portrait of an oscillatory system?
I am trying to plot a phase plane portrait of the following system:
dQ/dt = v*(z - Q)*(w^2 + Q^2)/(1 + Q^2) - Q
dz/dt = k - Q
where v = 1, k = 0.2, and w = 0.05.
So far, I have the following:
...
4
votes
1answer
212 views
Fit: Experimental`NumericalFunction error when fitting a black-box function
Bug appearing in at least 12.0.0 and 12.3.1
I'm trying some multidimensional Chebyshev fits. First, define a wrapper to prevent premature symbolic evaluation (I don't want a power series result):
<...
-1
votes
1answer
102 views
How to solve that logarithmic equation? [closed]
I mean an equation
$$ \log _{2 \sqrt{\sqrt{3}+2}}\left(x^2-2 x-2\right)=\log _{\sqrt{3}+2}\left(x^2-2 x-3\right).$$
The result of
...
27
votes
1answer
696 views
Efficient multidimensional optimization while constraining some coordinates
I have a function f[x] with a high-dimensional vector input and a scalar output. I am looking to minimize this function while constraining some of the components of ...
1
vote
2answers
101 views
NMinimize incorrectly says "The problem is unbounded"
I am solving some quadratic optimization problems in Mathematica 12.2 using NMinimize. Mathematica incorrectly gives the error ...
5
votes
4answers
256 views
Any Mathematica techniques to calculate time takes to reach the equilibrium of a PDE solution
I am solving this PDE numerically (dimensions: spatial variable x and time t).
I know how to solve my problem numerically (for a given range of time). The solution reaches its equilibrium after a ...
0
votes
2answers
188 views
1
vote
0answers
67 views
How does Mathematica numerically evaluate Gaussian Hypergeometric function $_2F_1(a,b,c,z)$ where $a,b,c \in \mathbb{C}$ [closed]
Gaussian hypergeometric function $_2F_1(a,b,c,z)$ usually takes $a,b,c \in \mathbb{R}$ and $z \in \mathbb{C}$. But using Barnes integral representation, one can analytically continue the $_2F_1(a,b,c,...
0
votes
2answers
47 views
0
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0answers
53 views
Is it possible that NSolve gives the roots that the function is not (well-)defined at those points? (an example is given)
I have this function for reals values of $x$ for $2<x<3$.
$$f(x)=(3 \pi -2 x)^2 \sin \left(\frac{1}{2} \left(\csc ^{-1}\left(\frac{4 \pi (\pi -x) \csc \left(\frac{\pi ^2}{\pi -x}\right)}{4 x^2-...
1
vote
1answer
85 views
Is there any alternative for NSolve or Solve to obtain all the roots of the given function?
I have this function for reals $0<x<\pi$.
$$f(x)=(3 \pi -2 x)^2 \sin \left(\frac{1}{2} \left(\csc ^{-1}\left(\frac{4 \pi (\pi -x) \csc \left(\frac{\pi ^2}{\pi -x}\right)}{4 x^2-8 \pi x+5 \pi ^...
0
votes
0answers
39 views
How can I make sure if the given function has any roots which are not rational multiples of $\pi$?
I have this function for $0<x<\pi$.
$$f(x)=(3 \pi -2 x)^2 \sin \left(\frac{1}{2} \left(\csc ^{-1}\left(\frac{4 \pi (\pi -x) \csc \left(\frac{\pi ^2}{\pi -x}\right)}{4 x^2-8 \pi x+5 \pi ^2}\...
1
vote
2answers
87 views
NSolve unable to solve system of equations with domain specification
I have a system of two equations in two unknowns that I would like to solve with NSolve within a specified region.
However, while Mathematica solves the system if I omit the domain specification, it ...
0
votes
1answer
59 views
Issues with Nintegrate - different methods yielding different values (both giving warnings)
I am integrating the following function
\begin{equation}
\frac{1}{2d^{2}}\times\frac{\sqrt{\omega_{c}\left|t_1-t_2\right|}-\sqrt{\pi}e^{\frac{1}{\omega_{c}\left|t_1-t_2\right|}}\text{erfc}\left(\frac{...
0
votes
1answer
73 views
2
votes
2answers
62 views
surprised Rationalize will sometimes leave a Real unchanged [closed]
I was surprised that Rationalize will sometimes leave a Real unchanged even if the fractional part of the Real is well above zero.
...
1
vote
1answer
99 views
Solving non-linear BVP with NDSolve and shooting method [closed]
I'm trying to solve a set of non linear DAE with global constraint
$$k(x) \left(\frac{1}{40} \omega ^4 n(x)^2+\frac{2}{3}\right)-L \lambda (x)-\frac{2}{3}=0,\ \ n(x) \left(\frac{1}{40} \omega ^4 k(x)^...
2
votes
0answers
40 views
JordanDecomposition not evaluating
When there are very small differences between entries in a diagonal matrix, sometimes JordanDecomposition does not evaluate and gives an error message:
...
0
votes
3answers
322 views
Python recursive bisection algorithm to Mathematica
I've been sitting on this problem for a while and i am kind of stuck. I am pretty new to Mathematica and have been trying to implement a recusive Algorithm, which splits/bisects a list of items in ...
0
votes
1answer
34 views
7
votes
1answer
181 views
Around workaround
I'm testing Around for error propagation (v12.2), but it seems to be inconsistent.
Error results depend on the form. Am I missing something here?
Edit
Same results ...
2
votes
1answer
62 views
Custom Normalization for NDEigensystem
I am trying to solve the Laplace equation in polar coordinates
$$-\left(\frac{\partial^2\psi_n(r,\theta)}{\partial r^2}+\frac{1}{r}\frac{\partial\psi_n(r,\theta)}{\partial r}+\frac{1}{r^2}\frac{\...
1
vote
1answer
109 views
FindRoot with a big range
I have a variable sig that is related to the variables (b,zQ,zh) given by torootsig, so I ...
2
votes
1answer
126 views
How to think about the answer to Rationalize[-11.5, 1]
In the open source Mathematica implementation called Mathics, an issue was raised where Mathics computes Rationalize[-11.5, 1] as -12 rather than Mathematica which ...
0
votes
0answers
55 views
Numerical Investigation of two Component Reaction-Diffusion System with Perturbative Advection
I am given two coupled differential equations and try to analyze them numerically because as far as I know, there is no analytical solution known(only the steady-state on an infinite domain is known, ...
0
votes
2answers
86 views
Nested NIntegrate over a region: Numerical Integration not converging
I need to computed two double nested numerical integrals, of which one is defined over a specific region (e.g. a pentagon). I've tried to use a single NIntegrate with four variables, but the result is ...
0
votes
1answer
64 views
Composite function derivatives
I would like to calculate the numerical partial derivatives (numerical gradient) of this function:
...
3
votes
1answer
76 views
MeijerG function: numerical evaluation of its derivative
Mathematica does not evaluate the derivative of the following MeijerG function.
...
1
vote
1answer
160 views
NonStandard finite difference for BMBB equation
I am trying to implement the following scheme mentioned in the paper
"NUMERICAL SOLUTIONS OF BENJAMIN-BONA-MAHONY-BURGERS EQUATION VIA
NONSTANDARD FINITE DIFFERENCE SCHEME
"
What is ...
2
votes
3answers
300 views
How to ask Mathematica to subtract each adjacent pair in a list, and then, sum them?
If I have a list of numbers as (the number of elements in this list is even)
list={1,23,32,54,65,76,87,98,109,110,...}
How can I ask Mathematica to subtract each ...
1
vote
0answers
54 views
logit ScalingFunctions
Having learned how to make symlog axes in this question, I was interested in the logit scale, the transforms of which are
...
0
votes
0answers
44 views
Indexing of NDEigensystem Result on a Cluster
I am trying to run on a cluster (where the version 11 of Mathematica is available) a code involving the following calculation:
...
1
vote
0answers
50 views
NDSolveValue BVP that encounters infinity
Problem setup:
I'm trying to solve the following, quite hairy, first order BVP problem, with four unknown functions $\phi, \theta, p_\phi, p_\theta$, and boundary conditions at $\phi(0), \phi(1), \...
