Questions tagged [numerics]
Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.
1,812
questions
2
votes
2answers
60 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.
...
0
votes
1answer
75 views
Solving non-linear BVP with NDSolve and shooting method
I'm trying to solve a set of non linear DAE with global constraint
$$k(x) \left(\frac{1}{40} \omega ^4 n(x)^2+\frac{2}{3}\right)-L \lambda (x)-\frac{2}{3}=0,\ \ n(x) \left(\frac{1}{40} \omega ^4 k(x)^...
2
votes
0answers
38 views
JordanDecomposition not evaluating
When there are very small differences between entries in a diagonal matrix, sometimes JordanDecomposition does not evaluate and gives an error message:
...
0
votes
3answers
263 views
Python recursive bisection algorithm to Mathematica
I've been sitting on this problem for a while and i am kind of stuck. I am pretty new to Mathematica and have been trying to implement a recusive Algorithm, which splits/bisects a list of items in ...
0
votes
1answer
34 views
7
votes
1answer
178 views
Around workaround
I'm testing Around for error propagation (v12.2), but it seems to be inconsistent.
Error results depend on the form. Am I missing something here?
Edit
Same results ...
2
votes
1answer
56 views
Custom Normalization for NDEigensystem
I am trying to solve the Laplace equation in polar coordinates
$$-\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
101 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
102 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
50 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
82 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
60 views
Composite function derivatives
I would like to calculate the numerical partial derivatives (numerical gradient) of this function:
...
3
votes
1answer
73 views
MeijerG function: numerical evaluation of its derivative
Mathematica does not evaluate the derivative of the following MeijerG function.
...
1
vote
1answer
132 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
286 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
51 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
39 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
47 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), \...
4
votes
2answers
257 views
How does mathematica numerically evaluate the Meijer G-function?
The Meijer G-function is defined as a contour integral in the complex plane. Mathematica is able to numerically evaluate such a function quickly and accurately. How does she do that?
2
votes
0answers
34 views
Supply gradient to FindMinimum subject to constraints
FindMinimum supports explicitly supplying the gradient (as well as the Hessian) via the Gradient (resp. Hessian) option. However,...
2
votes
0answers
63 views
NSum complaining of being non-numerical
I am trying to evaluate the sum $\sum_{k,l=1}^{30}\frac{1}{(k^2+l^2+1)^{5/4}}$ so I write
NSum[1/(1 + k^2 + l^2)^(5/4), {k, 1, 30}, {l, 1, 30}]
but I get a message ...
1
vote
0answers
46 views
2
votes
1answer
51 views
Passing a Piecewise function of NIntegrate through NIntegrate?
I am trying to pass a piecewise numerical integral (function1) through another numerical integral (function2). When I try this, however, I receive an error that says "t = T is not a valid limit ...
1
vote
1answer
49 views
Passing ParametricNDSolve through NIntegrate?
I am trying to integrate (function2) an integrand (function1) that is a function of a ParametricNDSolve output (solution1). This somehow works if I use ...
0
votes
0answers
76 views
Numerically integrating interpolating function whose initial conditions vary?
I am trying to numerically integrate--with respect to t0--an integrand (entitled function1 below) that involves an NDSolve interpolating function whose initial conditions are a function of t0. When I ...
2
votes
0answers
102 views
Approximate integer factorization
Suppose we would like to compute an approximate prime factorization of a large integer x in the sense that the difference between ...
5
votes
1answer
121 views
Accurately computing $\sum_{j=2}^\infty \frac{(-x)^j}{j!} \zeta(j)$
I'm doing a sanity check of the following equation:
$$\sum_{j=2}^\infty \frac{(-x)^j}{j!}\zeta(j) \approx x(\log x + 2 \gamma -1)$$
Naive comparison of the two shows a bad match but I suspect one of ...
1
vote
0answers
54 views
Alternatives to NumericQ that allow symbols to be considered numeric
I am writing a program in which I am using NumericQ. I am trying to allow symbols to also be considered Numeric, so I have been using NumericQ[a]=True for all of ...
2
votes
1answer
44 views
N::meprec warning when setting precision
How come
N[ Log[ Cos[1]^2 + Sin[1]^2 ] ]
evaluates to 0. without any trouble, while
...
5
votes
1answer
189 views
Airy function zeros, conflict (error?) between Wolfram Functions vs. Mathematica
According to functions.wolfram.com, the zeros of the Airy function $\operatorname{Ai}(z)$ occur at $z_k=f\left(\tfrac{3\pi}{8}(4k-1)\right)$ for $k\in \mathbb{N}$ where
$f(d)=-d^{2/3} \left(1 + \frac{...
0
votes
0answers
45 views
Instability in NIntegrate
I am solving the following equation with NIntegrate. However, the solution branches off at a certain time instance. When I increase the time step size, the instability occurs at larger time instant. ...
0
votes
1answer
62 views
Numerically solve 2nd order differential equations:
I'm trying to solve these two coupled 2nd order differential equations, but I'm getting nowhere. Mathematica can't seem to solve these no matter what I do. The equations are:
The $r_{*}$ is the value ...
1
vote
0answers
47 views
Solving a non-linear Schrödinger equation
I am trying to use NDSolve to solve numerically the well-known Schrödinger-Newton equation for a certain initial value of the wave function.
...
2
votes
2answers
214 views
'gradient' function in MMA
How to calculate Numerical gradient of 2D arrays using the "gradient function" ("Matlab-like")?
"[___] = gradient(F,hx,hy,...,hN) specifies N spacing parameters for
the ...
5
votes
4answers
159 views
Are there any alternatives for NIntegrate to calculate the area for which $f(x,y)<0$?
I have this two-variable function
$$f(x,y)= (8 \cos (x+y)+7)\cos \left(\frac{x}{2}\right)+\cos \frac{x-2 y}{2}+2 \cos \left(\frac{3 x}{2}\right) $$
where $0<x,y<\pi$. I want to calculate ...
2
votes
1answer
79 views
how to solve matrix differential equation using Mathematica
I have to solve $[m]x''+[c]x'+[k]x=[p]$
where x is function of $t$
after defining $[m],[c],[k]$ and $[p]$ in mathematica and
x[t_]={x1[t],x2[t],x3[t]}
I am using ...
0
votes
0answers
44 views
Problems with NSolve[] finding zeros of a 32-degree polynomial
I have the following calculation in Mathematica:
...
0
votes
0answers
94 views
FindRoot::dfmin: The minimal damping factor of 1/10000 has been reached
I have to solve a highly nonlinear parametric system of three PDEs.
I don't know to which extent the results are trustable. Indeed, the graph shown
by ParametricNDSolve also presents the error message ...
0
votes
1answer
36 views
How to make first component of eigenvectors on grid real and normalize using Map and Normalize? [closed]
I am trying to use the following approach: How get eigenvectors without phase jump?
to apply the same conditions to an array of complex-valued Mathematica eigenvectors.
The matrix solved for is a <...
1
vote
1answer
100 views
Repeating and Sequencing Procedures with two Do-loops
I have a Do loop where I'm looking for the value of certain parameters that respect the conditions inside an If, and with those values, a run another Do to make another calculation of an expression ...
0
votes
1answer
150 views
How do you calculate the area of a surface with edges in mathematica
Like the title indicates, how could I achieve this. Normally what I did for a closed surface is as follows:
...
5
votes
1answer
103 views
What are the best ways to compare numerical and exact solutions in 3D plots?
What are the best ways to comparing numerical and exact solutions in 3D plots?
For example, suppose that I have have numerical and exact solutions as follows:
...
1
vote
0answers
56 views
Non linear PDE solution
Could someone advise if it is possible to solve the following PDE with Mathematica? I am quite a beginner in Mathematica so any input would be highly appreciated.
$\displaystyle\frac{1}{2} \sigma^2\...
5
votes
1answer
132 views
How to plot solutions of a system of equations by changing colours when one of the variables increases by step?
I have a system of two 3-variable equations $SysEqs=\{f(x,y,z)=0\;,\;g(x,y,z)=0\}$ where the domain of variables are
$$6 < x < 2 \pi \\
- \frac{15}{100} < y < 0\\
0 < z < \frac 32$$
...
4
votes
1answer
188 views
Gradient of the numerical solution of a PDE
Solving the following PDE, defined in the same domain of a previous question:
...
0
votes
1answer
34 views
Numerical derivative (ND) not working for orthonormalized eigenvectors of a matrix
I have problem making ND work.
Define relevant needs and vectors
...
0
votes
1answer
128 views
_?NumericQ inside NDSolve to speed up code
I've seen some people using _?NumericQ to prevent symbolic calculation and speed up NDSolve.
Why in this simple code is not ...
4
votes
0answers
158 views
Numerical backward induction -- Solving sequential Cournot
I'd like to numerically solve a sequential Cournot competition in which supplier 1 moves before supplier 2, then the manufacturer sources from them, and finally sells the item at market clearing price....
1
vote
1answer
105 views
WhenEvent how to handle events at the same time and detection order
I need to use WhenEvent inside NDSolve in which events happen simultaneously.
I show simple code to better explain my question:
...
0
votes
0answers
38 views
Free boundary condition for American Option using Mathematica NDSolveValue
Was wondering if there is a Mathematica example solving the free boundary condition for American Option using NDSolveValue (free boundary condition is continue to hold v.s. early exercise of the ...
