All Questions
Tagged with mathematica numerical-methods
43
questions
-2
votes
0
answers
52
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Numerically solved PDE of Ornstein–Uhlenbeck process on 2-Simplex violates conservation of probability [closed]
Thanks for your consideration.
I'm working to create a solution of an Ornstein-Uhlenbeck process with a force that takes mass towards the centre of a Simplex. I'm assuming absorbing boundaries.
The ...
- 15
0
votes
0
answers
74
views
Software packages to compute finite type invariants of Polygonal Knots
Assume I have a polygonal knot, $K$, represented as its set of vertices $\{\mathbb{v}_i| \mathbb{v}_i\in\mathbb{R}^3\}_{i=1,...,n+1}$, where $n$ is significant, let's say $100<n<500$.
Which ...
- 51
0
votes
0
answers
22
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Radial wavefunction at origin for excited states $|{R_{nl}}^2| (0)$ for quarkonium
I am solving the radial Schrodinger wave equation for quarkonium containing a quark and antiquark. The system is non-relativistic as quarks are charm and bottom which are heavy. The wave equation is ...
- 1
0
votes
0
answers
71
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Evaluating Function of Incomplete Elliptic Integrals
I am trying to write Mathematica code that evaluates the following function:
$$
f(\kappa_{yx}, \kappa_{zx}) = 1 + 3 \kappa_{yx} \kappa_{zx} \frac{E(\varphi \backslash \alpha) - F(\varphi \backslash \...
2
votes
1
answer
241
views
How to solve this biharmonic equation? (Viscous fluid flow)
I am investigating lid-driven cavity flow, demonstrated in the below diagram:
We have a square (two dimensional) domain, with fully Dirichlet conditions for the velocity and fully Neumann conditions ...
- 12.5k
0
votes
1
answer
102
views
Numerically integrating $\int_{20}^\infty\frac{4^{1+4ix}\Gamma(-4ix)e^{-2ix}}{(-2i)^{-4ix}}dx$
I want to compute the following integral numerically in Mathematica,
$$\int_{20}^{\infty} \frac{4^{1+4ix}\Gamma(-4ix)e^{-2ix}}{(-2i)^{-4ix}}dx$$
The problem is that when evaluate the integral from $20$...
- 31
1
vote
0
answers
83
views
Conditions on the coefficients that the roots of a polynomial be less that or equal to unity in absolute value
Consider the polynomial $$f(x)=p_0x^n+p_1x^{n-1}+...+p_{n-1}x+p_n,~p_i \in \mathbb C.$$
Particularly, in the case of absolute stability of a multi-step numerical method, how can we find out the ...
- 2,184
7
votes
0
answers
424
views
A generalization of Elon Musk's favorite interview question (Going 1km South, 1km West, then 1km North returns to the starting position).
This question concerns a generalization of the following problem (allegedly, in the early days of Tesla and SpaceX, Elon Musk would ask the following question to possible future employees):
Assume ...
- 15.4k
0
votes
1
answer
100
views
Numerical integration of an integral with singularity
I am trying to solve this integral numerically using Mathematica. Here is my integral
$$\int_0^{\infty} dx\;\frac{\Gamma(\delta-4ix)}{(i(x-1)+\epsilon)^{1-4ix}}\;,
$$
where $0<\delta,\ll 1$ and $0&...
- 31
1
vote
1
answer
71
views
Continuation of Hypergeometric Function when $a - b$ is natural number
I am currently implementing the 2F1 Gaussian hypergeometric function numerically, and need to know its continuation for $ |z| > 1 $.
I have researched this and found this nice formula in the ...
- 43
0
votes
1
answer
107
views
Numerically Solve PDE
I am looking for some help finding a numerical solution to a pde of the form:
$$C_t=f(x)C_x+\alpha C_{xx}$$
with initial condition for $C(x,t)$:
$$C(x,0)=\delta(x)$$
and boundary condition
$$C(\pm\...
- 119
3
votes
1
answer
139
views
How to do a fast numerical computation of an oscillatory integral including $\operatorname{HeunC}$ function using Mathematica?
I am trying to numerically compute the following integral in Mathematica
$$\int_{1}^{1000} dx \,(x+2)e^{-2Ia(x+2)}\operatorname{HeunC}[-4Ib,-4Ib,1+4Ib,1,-4Ib,-x/2]$$
where $\operatorname{HeunC}$ is ...
- 31
1
vote
0
answers
91
views
Solving coupled integral equations
I would like to solve coupled integral equations of following form:
$$
\begin{cases}
f(0,n) = 1 + \displaystyle\int\limits_{0}^{\infty} K(n,p)f(1,p)dp \\
f(1,n) = g(n) + \displaystyle\int\limits_{0}^{...
0
votes
2
answers
90
views
Numerical solution of a linear differential equation with non-constant coefficients
I'm trying to solve the following linear differential equation with non-constant coefficients involving algebraic functions.
$\frac{d \phi}{d t}+\frac{ \left(\Delta ^2 \tau ^2-4 i \tau \sqrt{\Delta ^...
- 121
2
votes
1
answer
176
views
On the function $\chi_{\{x \le F(y)\}}(x,y)$ where $F$ is Lipschitz
Let $F:\mathbb{R} \to \mathbb{R}$ be a $L$-Lipschitz function.
Consider the function
$$G(x,y) = \chi_{\{x \le F(y)\}}(x,y),$$
where $\chi$ is the indicator function.
How can I plot this function ...
- 297