Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.
0
votes
1answer
33 views
FindMinimum gives wrong solutions inside a loop
I have a density function $\rho(r,z)$ and I want to calculate the minimum distance $d_{min} = \sqrt{r^2 + z^2}$ from the center (0,0) in which $\rho$ becomes negative. The easiest way is to find where ...
0
votes
0answers
132 views
Numerically solving system of partial differential equation
I am trying to solve a system of partial differential equation with boundary conditions. But I got an error message saying NDSolve::icfail: Unable to find initial ...
0
votes
0answers
69 views
Is there a way to generalize FindAllCrossings3D to higher dimensions?
I understand the obvious visualization issues, but is there a way to extend the argument to higher dimensions, ie more equations?
0
votes
1answer
88 views
Gram-Schmidt process with Hermite functions on [-1, 1]
Denote by $h_n$ the $n$-th Hermite function.
$$
h_n(x) = \frac{(-1)^n }{\sqrt{2^n n! \sqrt{\pi}}} \mathrm{e}^{\frac{x^2}{2}} \frac{\mathrm{d}^n}{\mathrm{d} x^n} \mathrm{e}^{-x^2}
$$
I am trying to ...
6
votes
1answer
221 views
Minimization by Nelder-Mead
Finding a global minimum for this problem (non-linear optimization by the Nelder-Mead downhill simplex method) may not be possible, but by finding local minimum, I am expecting the value of the ...
4
votes
2answers
144 views
Why doesn't FindRoot work correctly?
I'm trying to find the roots of the following equation:
I need to find λs for different values of ξ. I know that for all ...
5
votes
1answer
59 views
Why is NHoldFirst not propagated to symbolic derivatives?
I encountered a nasty problem that N cannot evaluate expressions containing a symbolic Derivative of a multi-parameter function ...
-3
votes
0answers
33 views
Directly proportional Question [closed]
Mr Tan’s monthly savings (S) is directly proportional to the square root of his monthly income (I). His income in January and February 2011 is 3600 and 2500 respectively. His savings in January is 80 ...
31
votes
3answers
653 views
When I can assume that all decimal digits returned by Mathematica are provably correct?
How to Control the Precision and Accuracy of Numerical Results
Arbitrary-Precision Numbers
Mathematica works with exact numbers and with two different types of approximate numbers: ...
2
votes
2answers
183 views
0
votes
1answer
55 views
How to convert Approximate number to exact Fractions? [closed]
When solving certain equations Mathematica warned of using approximate numbers, and does conversion to exact number by default, followed by yet another conversion back to approximate results, like
...
-2
votes
0answers
56 views
Problem in evaluating numbers [closed]
I have some problem evaluating numbers.
I have this instruction (H is an Hamiltonian), and I want my system to evolve to a certain state.
...
5
votes
1answer
94 views
Accurately evaluating the hypergeometric function
As part of another problem, I am working to evaluate hypergeometric functions such as
Hypergeometric2F1[1, 1, n, -1]
for large $n$. I am hoping to obtain at ...
3
votes
1answer
71 views
Monitoring the Evaluation of NDSolve: time to finish estimation
My problem is quite simple: I run a NDSolve with a system of many ODEs, a calculation that will run for many hours, and I would like to know the progress of the ...
7
votes
1answer
129 views
Computation of Hankel Transform using FFT (Fourier)
To address circular symmetric cases of 2D Fourier Transformations the so called Hankel Transform can be applied (for a detailed derivation of the relation between the 2D Fourier transform and the 1D ...
0
votes
0answers
56 views
Initializing Minimization [duplicate]
I am trying to implement a model predictive control scheme in Mathematica, e.g. I optimize input sequences by predicting future outputs. So every time I call the cost function it will simulate the ...
1
vote
1answer
46 views
Set theoretic operations on sets of real numbers
I have two pieces of code that produce a bunch of real numbers, say $A$ and $B$ respectively. (It is not relevant to the question, but $A$ consists of eigenvalues of the Hamiltonian of some physical ...
0
votes
1answer
79 views
Plotting the Bessel function with a float argument [closed]
The equation I am working with is
$$ E = M_e + \sum_{n = 1}^N\frac{2}{n}\mathcal{J}_n(ne)\sin(nM_e) $$
where $\mathcal{J}_n(x)$ is the nth Bessel function of the first kind.
When I enter the ...
4
votes
0answers
101 views
Numerical solution of Schrödinger-type equation in Mathematica [duplicate]
I want to solve the following differential equation numerically:
\begin{equation}
i\partial_{t}\psi(r,t)=\left[-\frac{\Delta}{2m}+g\left|\psi(r,t)\right|^{2}+V_{d}(r,t)\right]\psi(r,t)
\end{equation}
...
1
vote
3answers
74 views
How to calculate solution for each variable automatically
Here I have one problem how to calculate x for each y. In this form code doesn't work
...
1
vote
3answers
103 views
Making a calculation with high precision
I would like to make the following calculation:
1/Sqrt[1 - (150^2 10^(-4))/(9 10^16.)] - 1
Mathematica 8 returns 0. The result is obviously not 0, but my ...
2
votes
0answers
69 views
Speeding up a numerical constrained quadratic optimization
I'm trying to solve a quadratic optimization problem in 35 variables, $\vec{α} = \left< α_1, \ldots, α_{35}\right>$:
$$
\begin{aligned}
&\operatorname*{maximize}_\vec{α}&&1.0\cdot ...
2
votes
2answers
111 views
2
votes
0answers
31 views
NIntegrate/NSum with parameters [duplicate]
I'm trying to calculate a continuous integral within a discrete integral.
Something similar to this (yet more complex):
...
0
votes
1answer
168 views
DAE - varying initial conditions
I want to solve a DAE-system and I want to vary more than one initial conditions and to manipulate them. I looked here:
Putting NDSolve into ParametricPlot
But it does not work:
...
4
votes
2answers
110 views
0
votes
1answer
70 views
0
votes
0answers
63 views
7
votes
0answers
172 views
Numerically solve 2nd order differential equation with singularity
Consider a second order differential equation with a potential that diverges at some generic value in the variable. For example:
$$-y^{\prime\prime}(s)+\frac1{\mathrm{cn}{(s\mid k^2)}}y(s)=0$$
where ...
29
votes
1answer
529 views
10
votes
1answer
241 views
Why can't I change the value of MaxRecursion in NIntegrate when integrating BesselJ?
I am trying to evaluate this integral numerically
$$
\int_0^{\infty } J_0(q R) \tanh(q) \, \mathrm{d}q
$$
for large values of $R$. This makes the integrand oscillate more quickly and Mathematica ...
1
vote
1answer
172 views
Why is arithmetic faster for inexact arithmetic?
I have been trying to compute eigenvalues of a rather sizable matrix A, about $500 \times 500$ (but sparse). I asked Mathematica to compute ...
1
vote
1answer
105 views
why there is a small imaginary part [closed]
I encountered a problem. I have a eigenvector eigvsI[1]
...
4
votes
1answer
77 views
Minimize failing on a polynomial
Calling:
Minimize[{-0.4877 - 0.1190 r^2 - 0.1885 r^4 + 2.9703 z - 0.5531 z^2,
0 <= z <= 3.5 ∧ 0 <= r <= 1.75}, {r, z}]
returns ...
1
vote
0answers
142 views
Adapting NDSolve to circumvent NDSolve::bdord: error for 1-D Euler Equations
I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a ...
3
votes
0answers
145 views
FindRoot gives a wrong solution which obviously should not be there
I got stuck on FindRoot and I didn't see any similar problem posted, so let me explain what I am trying to do and what problem I meet here.
I try to find roots of a particular function, which in the ...
0
votes
0answers
49 views
How to force evaluation/numerical result of a function? [closed]
I defined a function m[x] using
...
3
votes
1answer
208 views
NDSolve for a large system of simple ODEs
I am solving a system of many (more than 100) ODEs.
It is the kind of standard rate equation encountered in semiconductor physics.
Here is the system:
...
13
votes
1answer
332 views
Optimizing a Numerical Laplace Equation Solver
Laplace's Equation is an equation on a scalar in which, given the value of the scalar on the boundaries (the boundary conditions), one can determine the value of the scalar at any point in the region ...
1
vote
1answer
87 views
Plot FindRoot for non-trivial function
I would like to plot the results of FindRoot over certain range of inputs. I tried to do this with the code:
...
3
votes
1answer
78 views
Find point at which equation stops having roots (if it exists)
I am interested in the roots of this function:
f[M_, b_] := 1 - (2 M Gamma[2, 0, (1/M + b M)/Sqrt[b]])/(1/M + b M)
for fixed values of b. In particular I want ...
1
vote
2answers
143 views
How can I use FindRoot on an expression from NDSolve?
I have a second order ODE that I can only solve numerically using NDSolve, but I then need to use the solution in FindRoot and am running into errors. A simplified but analogous problem is the ...
0
votes
0answers
68 views
FindMaximum inconsistency
The code below seems to work for n<11. But for n=11, and above, it outputs newa then just outputs "beep" sound.
WhyTheBeep says "The kernel Local has quit ...
0
votes
1answer
101 views
How to guess initial complex value for FindRoot
I have to solve a transcendental equation for a parameter, say $\beta$. Now, the $\beta$ has a range from $ik$ to $k$ where $i$ is the usual imaginary root $\sqrt{-1}$ and $k$ is a real number. ...
3
votes
1answer
207 views
Tutorial for basic numerical methods for PDEs
I'm afraid this is probably not going to be a "good" question, but I'd like to use Mathematica to learn about basic numerical schemes for solving pdes. For example, I'd like to compute the solution of ...
1
vote
0answers
66 views
Using Root for numerical evaluation [closed]
In my expressions I have a lot of roots to calculate. For example:
Root[#1^3 + #1^2 + #1 &, 1]
Since most of them cannot be solved analytically, I would like ...
0
votes
0answers
374 views
Jacobi eigenvalue and eigenvectors algorithm
Suppose we have a symmetric matrix with dimensions n x n. I need to find the eigenvalues and eigenvectors of this matrix using the Jacobi method. I wrote this code:
...
0
votes
0answers
88 views
Speeding up numerical computations
So, after seeing this and this post, I was thinking whether there were any general rules for speeding up numerical computations (not only NIntegrate or ...
3
votes
1answer
80 views
Numerical Error with Large Matrices
I am writing a Finite Element Analysis program in Mathematica. The code involves handling a large matrix with large entries. I get an error when I try to use Mathematica's "LinearSolve" to solve a ...
0
votes
1answer
162 views
Minimization problem using FindMinimum. Functional value “is not a real number”? [closed]
This question is a follow-up of another one I asked a few days ago. I followed the instructions given in the answer provided by the user that responded. I modified that answer to solve another ...
