Questions tagged [complex-analysis]
The complex-analysis tag has no usage guidance.
12
questions
5
votes
1answer
140 views
Complex differentiation of linear solvers
I have a linear system $$Ax=b$$ which I'm solving approximately, and I need to take the frechet derivative of x with respect to z. Were I solving the problem exactly (either analytically or to machine ...
4
votes
0answers
96 views
MATLAB: Compute the Schwarz-Christoffel transformation symbolically
Suppose we have a conformal mapping from the unit disk in the $\omega$ plane onto the exterior of a polygon in the $z$ plane.
The Schwarz-Christoffel mapping in this case is defined as:
$$f(u) = A - ...
11
votes
1answer
162 views
Numerically Recovering Imaginary Part of Analytic Continuation from Real Part
My situation.
I have a function of a complex variable $f(z)$ defined through a complicated integral. What I am interested in is the value of this function on the imaginary axis. I have numerical ...
3
votes
3answers
126 views
How to calculate $\arg(z_1z_2\cdots z_n)$ to minimize results error?
As in title, which method is the most optimal for numerical calculating value of:
$\arg(z_1z_2\cdots z_n)$?
Method 1: one can first calculate $Z=z_1z_2\cdots z_n$ and then calculate $\arg(Z)$.
...
4
votes
0answers
67 views
Complex Integral Equation Solution in MATLAB
I need to solve an integral equation in the form:
$$A(z)+\int\limits^{z_2}_{z_1}B(z') \frac{z^N}{z^N-z'^N} \frac{e^{i\beta}}{|z|}\mathrm{d}z'=0 $$
where $A(z)$ distribution is known and we are ...
2
votes
1answer
765 views
Complex Numerical Integration using GSL
I want to program an integration routine in C++ using the GSL library but for complex functions.
How should I split my integrand to apply the gsl_integration_qag function on it.
Just integrate the ...
1
vote
1answer
135 views
Applicable solvers for nonlinear coupled PDEs
I've been trying to find an applicable PDE solver for cases such as this:
Although when dealing with stiff equations in the complex domain, applying existing packages has been problematic.
I've ...
7
votes
1answer
103 views
Are there special methods for solving $f'(z)=0$ for analytic $f$?
I am trying to solve a bunch of equations for the zeros of the derivative of an analytic function, and I would like to know if there exist methods that exploit this structure to provide better ...
2
votes
0answers
58 views
Need a smart way to numerically take residues in a multidimensional integral
I'm trying to do an integral of the form $\int_C f(u,v) $, where $C$ is a set of contours in $u$ and $v$. In particular, each variable's contour starts at $-\infty+i \epsilon$, goes around a branch ...
6
votes
2answers
197 views
Continuation procedure to solve for a 2D curve that satisfies f(x,y) = 0
I have some function of $R^2$, that must be numerically computed. For instance, I might be interested in a real-valued contour integral that begins from (x,y) = 0.
$$
f(x,y) = \Re\left[\int_0^{x + iy}...
0
votes
1answer
213 views
Drawing 3d projection of complex surface
I have a complex surface (real dimension 2) in $\mathbb{C}^2$ with coordinates $(z,w)$ given explicitely: for any $\xi \in \mathbb{C}$ I know points $w(\xi)$ of intersection of surface with complex ...
15
votes
1answer
1k views
How to numerically calculate residues?
I need to calculate the following integral:
$$
{1\over 2\pi i} \int_C f(E) \, d E
$$
$$
f(E) = {\rm Tr}\,\left(({\bf h} + E)\,{\bf G}(E) \right)
$$
Where $\bf h$ is a matrix (one particle kinetic and ...
