Tagged Questions
Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.
1
vote
0answers
42 views
How to solve a stiff non-linear differential equation?
I am having trouble solving the following differential equation, where $\theta(x)$ is a phase,
\begin{equation}
\frac{d\theta}{dx} + \sin^2 \left[ \theta(x) \right] + K^2(x) \cos^2 \left[\theta(x) \...
4
votes
3answers
90 views
3
votes
2answers
84 views
+50
Getting additional control over MaxRecursion/PlotPoints
I'm occasionally in a position where I need to compute a RegionPlot with some small area of the plot being computationally much more expensive then the rest of the ...
0
votes
0answers
31 views
1
vote
1answer
48 views
How can I solve this non linear system of ODEs using NDSolve?
I want to find solutions to the system:
$$\begin{align*} -2b'(s)\sin(b(s)) &= \sin(b(s))(a'(s)b''(s) - a''(s)b'(s)) - (a'(s))^3 \sin^2(b(s))\cos(b(s)) \\ &(a'(s))^2\sin^2(b(s))+(b'(s))^2 = 1\...
1
vote
1answer
51 views
How to represent in a 3D graph the set of solutions to this system of inequalities?
I am studying this piecewise function:
...
5
votes
0answers
47 views
Details of NDSolve calling LSODA
Inspired by my question regarding the computation time of NDSolve using the LSODA backend I was wondering how NDSolve is actually calling LSODA (what arguments are sent to LSODA), i.e. what are the ...
0
votes
1answer
44 views
Numerical Approximation of erfc
I have a crazy output. I already tried the N[] function. All it does is condense the inputs. Any idea of how to have a numerical output from the code?
0
votes
0answers
29 views
Numerical error General::munfl: encountered in a simple computation
There is a similar General::munfl: error in Mathematica 11.3.0, where it occurs when computing Log[Exp[-800.`]].
But in my code,...
2
votes
2answers
49 views
NDSolve producing message Power::infy
I am trying to solve geodesic equations in some 3D black hole spacetime. It is a coupled ODE system with boundary conditions. Due to the symmetry of the spacetime, I expect the solutions to be even ...
2
votes
0answers
85 views
Derivative of an interpolation function is noisy
I have a set of numerical data of 1501 points, in the form of $\{x_i,a_i\}$ which I uploaded to here and here.
I need to compute the numerical derivative of this data. In particular, I need the ...
3
votes
1answer
106 views
Newton's Method
Problem statement:
I'm currently new to Mathematica and have been trying to solve this problem. I was digging around and found this code:
...
0
votes
0answers
34 views
1
vote
1answer
73 views
How to get solutions for this system of inequalities?
I am new to Mathematica and I am struggling finding the solution for the following problem.
I am studying this piecewise function:
...
1
vote
0answers
21 views
Inverse of Normal Distribution CDF incorrect for large value?
I have a function F which is the CDF of the standard normal distribution. The inverse of F should be infinity at 1. However, I ...
3
votes
0answers
128 views
On Ж, and the fine-structure constant
I'm trying to reproduce the results from a certain infamous paper that has been moving around the web for the last few days. The details are irrelevant.
This paper claims to have a closed-form ...
2
votes
1answer
76 views
Computing numerically infinite sum of some double series
Let's consider the series:
$$
F(t) = \sum\limits_{n=0}^{\infty}\sum\limits_{k=0}^{\infty}
\frac{(-b)^k(-a)^n\binom{n+k}{k} t^{2n+k(2-\alpha)}}{\Gamma(2n+k(2-\alpha)+2)}
$$
where $a,b$ are ...
1
vote
0answers
65 views
Is it possible to solve following question about integer programming using mathematica?
Consider a $5$-uple $(r,a,b,c,s)$ with $a,b,c\in\mathbb{Z},s\in\mathbb{Q}_+,r\in\mathbb{Z}_+$, denote $\frac{1}{2}(a^2-b^2-c^2)-\frac{s}{r}$ by $\Delta(\mathbf{v})$.
Let $A$ be a positive real number....
14
votes
4answers
247 views
Terrible accuracy of DawsonF
DawsonF[30.] returns 0. The correct value is 0.016676...
At least it prints a warning message,
...
0
votes
3answers
78 views
Using WhenEvent to Change the Sign of a Constant
I am attempting to change the sign of a constant when a certain condition is met during a numerical integration. Here is the code:
...
5
votes
2answers
111 views
Integrating a bivariate distribution over a region bounded by a straight line
Summary of problem: I'm using Mathematica version 8 to try to integrate the bivariate distribution over a region bounded by a straight line. The two random variables are uncorrelated. When I use ...
2
votes
1answer
52 views
Taking a derivative of an eigenvector
I'm trying to calculate the derivative of an eigenvector that I obtain by
...
1
vote
1answer
76 views
Help to extend this evaluation!
I'm performing a stochastic evaluation, where i'm interested in the assymptotic behavior of the solutions, but my computer can't stand very large times. So I thought that I could evaluate a certain ...
0
votes
1answer
44 views
Numerical solution of an ODE using NDSolve
I am to find the solution $R(\rho)$ to the following differential equation,
$\frac{\partial}{\partial\rho}\left(A^2\frac{\partial}{\partial\rho}R(\rho)\right)-l(l+1)R(\rho)=0$
where $A$ is a ...
0
votes
3answers
108 views
How to solve these equations numerically?
I have some differential equations as below. I have tried to solve them numerically with NDSolve:
...
0
votes
0answers
46 views
Solving differential equation (with numerically-inverted functions inside it)
I have a routine for numerically inverting a function and i want to inject this function (routine) into a differential equation. Now, i am solving the differential equation with DSolve but it just ...
0
votes
1answer
39 views
Solve PDE by using Spatial Discretization for two dimensional independent spatial coordinates
I have a code given by
...
2
votes
2answers
215 views
Solving 2D+1 PDE with Pseudospectral in one direction with periodic boundary condition?
According to the documentation about the pseudospectral difference-order:
It says:
Following the discussion here:
I found the messy behavior is always on the artificial boundary in $\omega$-...
0
votes
1answer
49 views
How can I plot the solutions to this system of non linear ODEs?
I need to solve the following system:
$$\left\{ \begin{array} { l l } { (u')^2 + (v')^2 = 1 } \\ {u'v'' - u''v' = uu' + vv' } \end{array} \right.$$
and it's a task that's proven to be quite hard by ...
-1
votes
1answer
62 views
Numerical Inversion of an incomplete beta function expressed as gauss hypergeometric function using Mathematica
I am currently working with this hypergeometric function ${_2}F_1$,
$\rho(r)=\frac{2b}{1-q}(1-(\frac{b}{r})^{1-q})^{\frac{1}{2}}{_2}F_1(\frac{1}{2},1-\frac{1}{q-1},\frac{3}{2},1-(\frac{b}{r})^{1-q})$
...
2
votes
0answers
41 views
What is the acceptable error in numerical calculations? [closed]
I am doing a calculation where I try to simplify a very complicated complex function. I did this step by step and I checked that the numerical values that the function gets for certain values of the ...
4
votes
2answers
162 views
2
votes
2answers
155 views
Unstable solution of 2D+1 time PDE with periodic boundary condition
Now I am trying to solve the following 2D+1 type of PDE:
$\partial_t u(t,x,y)=-y\partial_{x}u+\partial_{y}\left[a y+b sin(x)u+c\partial_{y}u\right]$
with $u(0,x,y)=\frac{1}{2\pi}e^{-((x-\pi/4)^2+y^2)...
0
votes
1answer
107 views
What is wrong with this MonteCarlo? [closed]
I am making a trial for a MonteCarlo. In this code I simulate 10 protons hitting on a slab of gold:
...
2
votes
1answer
72 views
How would one go about plotting this parameterized curve using numerical resources (analitically it's too hard)?
I'm working with the system of differential equations:
$$\begin{align*}
\left\{ \begin{array} { l l } { (u')^2 + (v')^2 = 1 } \\ {u'v'' - u''v' = -v' + u' } \end{array} \right. \end{align*}$$
Where $...
2
votes
1answer
71 views
Non-linear numerical solution with variable parameter
I have solved the following system non-linear:
...
3
votes
1answer
55 views
Machine Epsilon is not equal to $MachineEpsilon
I try to wrap my head around machine precision calculations in Mathematica (11.2, Linux). I do not understand the following behavior:
...
1
vote
0answers
31 views
Determine if nonlinear function can be positive subject to nonlinear constraints [closed]
I am trying to determine if a certain nonlinear function can be positive when the variables have to satisfy multiple nonlinear constraints.
Currently my code looks like
...
6
votes
4answers
113 views
Suppress trailing 0s in numerical values
For example, this is what I want
In[1]:= N[Table[4^(i/4), {i, 1, 4}]]
Out[1]= {1.41421, 2., 2.82843, 4.}
But if I want a few more digits only from the irrational ...
3
votes
2answers
140 views
Increase Performance of WhenEvent in NDSolve
I'm trying to reset the value of functions $u_{i}$ when they reach a threshold $θ$. Below the threshold, they evolve according to a simple differential equation. The $r_{i}$ resets the derivative to ...
2
votes
0answers
96 views
How to Solve this Fokker-Planck Equation?
I need to solve this Fokker-Planck equation in Mathematica and my attempt to perform this integration is above:
My first attempt is above:
...
0
votes
2answers
58 views
Computing a sum with high precision
I am aware that a similar question has been asked, for example, here and here, but none of the proposed solutions solves my problem, so please wait before you mark this question as a duplicate.
...
15
votes
1answer
206 views
What happened to SequenceLimit?
In older versions of Mathematica, there was a function called SequenceLimit that allowed taking the limit of a numerical sequence. It is useful for speeding up the ...
2
votes
1answer
43 views
FindMinimum finds a zero value for solving a system but does not converges. Can I interpret it as the solution for system?
I am solving a system of three non-linear equations for three unknowns. I am using FindMinimum to minimize the norm of residuals of the system. I have played a lot ...
1
vote
0answers
30 views
Solve the 'Eigenvalue' problem efficiently [closed]
Usually, an eigenvalue of a matrix A is defined as |A-b*I|=0, where I is the identity matrix and |..| is for the determinant.
Now my question becomes a little different, let's say A is a function of ...
3
votes
2answers
221 views
Solve PDE involving implicit function of independent variables
I have a differential equation given by
-4*D[S[u,v],u,v]==V[u,v]*S[u,v]
with boundary conditions
...
1
vote
1answer
36 views
Precision error in FindMinimum
I am trying to solve a system of three non-linear equations for three unknowns (e1, e2, phi). I am using FindMinimum to solve the system (I am minimizing the norm ...
1
vote
1answer
60 views
How to make Mathematica show small and large results? [closed]
I have two equations with x=r+Log[-1+r] and v=(1-1/r)/r^3 forms. When I substitute ...
3
votes
1answer
86 views
Problem with the function N with second argument
I was asked to look at a complicated definite integral that could be integrated analytically, but numerically did not behave as expected. After a lot of simplifications I arrived at the following:
<...
2
votes
1answer
55 views
How can NDSolve be used to get just the positive or just the negative energy solution to the Klein-Gordon equation?
The Crank-Nicolson technique below is obtained from:
"http://reference.wolfram.com/language/tutorial/NDSolvePlugIns.html"
...
