Widely used as a synonym for numerical-analysis, in particular in the German speaking community.

learn more… | top users | synonyms

0
votes
0answers
30 views

Unitary matrix representing Discrete Fourier Transform

Let $F_n\in\mathbb{C}^{n\times n}$ be the unitary matrix representing the discrete Fourier transform of length $n$ and so $F_n^{H}\in\mathbb{C}^{n\times n}$ is the inverse DFT of length $n$. For ...
5
votes
1answer
71 views

Are self-convergence tests reliable?

I'm developing a solver for solving linear hyperbolic equations of first order with respect to time and spatial derivatives. The formal order of accuracy of the solver must be 5 because I use ...
1
vote
0answers
67 views

Numerical inversion involved confluent hypergeometric (1F1) (or Kummer function)

Edit: the question is solved ! Thank you for your time ! This problem arises when I tried to compute the valua of Asian call otions using Inverse Laplace transform method. Let $r=\mu = 0.15; \sigma ...
6
votes
2answers
82 views

Sum over very small exponentials: Underflow

I am trying to compute (in C) a sum like $S = \sum_i \exp( - a_i )$, where $10^{4} < a_i < 10^{5}$ are approximately normal distributed. So even if I do the Log-Sum-Exp trick $S = ...
0
votes
0answers
45 views

convergence of one step methods, order $p$

This question is not homework it is recommended exercises to prepare for the final exam. Consider the family of linear one-step methods defined by $$y_n = y_{n-1} + h(\theta f_n + (1 - ...
1
vote
0answers
100 views

Family of linear one-step method convergence question

This question is not homework it is recommended exercises to prepare for the final exam. Consider the family of linear one-step methods defined by $$y_n = y_{n-1} + h(\theta f_n + (1 - ...
3
votes
1answer
107 views

How do I develop numerical routines for the evaluation of my own special functions?

This question was previously posted to Math.SE here and had received no answers at the time of this posting. When performing computational work, I often come across a univariate function, defined ...
3
votes
2answers
176 views

Does artifical dissipation term makes scheme inconsistent?

Central schemes like JST uses artificial dissipation for the stabilization. This modification is an artificial one. Does this additional term makes system inconsistent? Can we expect this term to be ...
1
vote
1answer
56 views

How do I add some floating point numbers, keeping numerical accuracy in mind?

I am solving a problem involving the line with the set of points $(x_3,y_3)$ that are equidistant to two given points $(x_1,y_1)$ and $(x_2,y_2)$. The equation for this line is $$(x_3 - x_1)^2 + (y_3 ...
2
votes
0answers
137 views

C++ library for numerical intergration (quadrature)

I have my own little subroutine for numerical integration (quadrature), which is a C++ adaptation of an ALGOL program published by Bulirsch & Stoer in 1967 (Numerische Mathematik, 9, 271-278). I ...
1
vote
1answer
55 views

Big errors while calculating Complex Cholesky Factorization

I am using my own Routine to calculate the Cholesky-Factorization of a complex, positive definite symmetric Matrix. My Code Looks like this: ...
3
votes
1answer
68 views

Numerical integration with singularities

I need to compute some integrals numerically. The integrand is this: $$f(x,y) = \left ( \sum_{mn=-j}^{j}A(m,n)\dfrac{\tan^{2j+m+n}(x/2)}{(1+\tan^2(x/2))^{2j}}e^{iy(n-m)} \right )^{N}$$ Note: sums ...
2
votes
1answer
92 views

Improving my QZ-Algorithm (Include Shifts)

I Need to to solve an generalized Eigenvalue Problem and to compare two Methods (QR and QZ) concerning their convergence rate and execution time. I started with the Basic QR-Algorithm, implemented in ...
2
votes
0answers
53 views

Difference between fast and normal Givens Rotations?

would someone be so kind as to explain me the difference between the ordinary givens-rotation and the fast givens-rotation? I know that the fast givens Rotation reduces the Count of operations to ...
3
votes
1answer
66 views

How close observed order of accuracy should be to theoretical order of accuracy?

I try to write tests to the implementations of numerical methods. The best way to do this is to study the observed order of accuracy and check that it matches with the theoretical order of accuracy. ...
1
vote
0answers
48 views

Jacobi method converging then diverging

I am working to solve Poisson's equation in 2D axisymmetric cylindrical coordinates using the Jacobi method. The $L^2$ norm decreases from $\sim 10^3$ on the first iteration (I have a really bad ...
3
votes
0answers
38 views

Broadening spectral data by using FFT's

I obtain numerical discrete data of the form $$ S_{raw}(\omega) = \sum_{j}w_{j} \delta(\omega-\omega_{j}) $$ to compare the result with experimental data the delta peaks need to be broadened ...
5
votes
1answer
57 views

Reference request: theory regarding time evolution of closed loop 2D elastic shapes?

I am interested in approximating the time evolution of 2D curves. Here's an illustration: An issue that arises when naively making this approximation as illustrated above, is that as one increases ...
6
votes
1answer
161 views
1
vote
1answer
41 views

Resources exploring the problem of “volume exclusion”?

Consider the following situation: There are two boundaries -- one is denoted using grey lines, and the other is denoted using black lines. The boundaries are numerically represented using ...
2
votes
0answers
46 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 ...
7
votes
3answers
279 views

What is the fastest opensource implementation of Bessel functions computation?

I'm looking for an open-source (to use and learn from) software which computes Bessel functions of integer order of real argument to double precision the fastest among all such implementations. ...
1
vote
1answer
77 views

Numerical quadrature when locations of singularities are approximate

I'd like to numerically integrate $\frac{1}{\sqrt{f(x)}}$ on an interval between two consecutive zeros of the function $f(x)$, which makes the integrand singular at two endpoints. Standard practice ...
2
votes
1answer
58 views

Resource recommendations for numerical methods involved in dynamical systems analysis

I am interested in learning numerical methods that specifically have to do with analyzing dynamical systems. In particular: drawing phase plane diagrams drawing phase portraits analyzing ...
0
votes
0answers
51 views

Quick scheme for separable first-order ODE

I'm trying to integrate an incredibly simple ODE: $$ y'(x) = -f(y),\quad y(0) = y_0 \ , $$ from $x=0$ to $x=1$. This is a decay type of equation, $f$ is the (variable) decay rate and $y$ is the ...
1
vote
0answers
108 views

Tips on improving stability in numerical scheme for non-linear PDE

I am solving a non-linear second order system of PDEs in two variables. The equations are too complicated to write out here, but an essential feature is that there is a propagating wave which then ...
0
votes
1answer
116 views

Numerical integration of sharp peaked function (position of peak known)?

What methods are available to integrate a sharply peaked function (position of peak known) on a finite interval (the interval includes the peak)? Currently I am getting underflows using some of GSL's ...
1
vote
1answer
124 views

Shallow Water Equations Boundary Conditions

I am trying to solve shallow water equations using DG methods. Flow over a bump is a common problem that comes up in this context. For example ...
4
votes
1answer
235 views

When and why is `r./sum(r)` not a good way to renormalize a vector in PageRank computation?

I experimented with the PageRank algorithm. When the number of pages is large, I encountered a situation when one formula for re-normalizing a vector (so that sum of its components is equal to 1; ...
1
vote
1answer
109 views

What does “strongly conservative” mean in the context of numerical methods?

I have a homework problem that asks me to show that 1st order unwinding or central differencing can give a strongly conservative, consistent scheme for the 1-D Burger's Equation using a finite volume ...
0
votes
1answer
236 views

How to solve Energy Balance equation by numerical method

Good Day I am new to heat transfer technique please give me some suggestion on solving energy balance equation $$a \frac{\partial T_p}{\partial t}=\frac{\partial}{\partial x}\left(b\frac{\partial ...
3
votes
1answer
137 views

How to integrate numerically a function with error bars?

Typically, the function that one wants to integrate numerically, $f$, is given, i.e. its values for various points $\{x_i\}$ are known precisely. The resulting error is due to the fact that we chose a ...
2
votes
2answers
100 views

Expected computational time for DNS computation of fluid flow

Using an established criterion involving capturing eddies down to the Kolmogorov length scale it can be reasoned that the order of grid points in the computational mesh needs to be $N^3 \ge Re^{9/4}$ ...
1
vote
0answers
130 views

Plotting renormalization group flow diagram from recursion relation

How do I plot a flow diagram (given certain initial conditions, the trajectory in y-x space) for a RG (renormalization group) flow given by the following recursion relations? \begin{eqnarray} ...
-2
votes
1answer
1k views

Runge-Kutta 4th order for 4 coupled first order differential equation [closed]

I have to solve 4 coupled first order differential equations for $f(t)$ ,$g(t)$, $h(t)$ and $w(t)$ witch are only functions of $t$ , but for every reference link a function of 3 variables is assumed ...
1
vote
1answer
41 views

Modifying finite difference solution to Schrodinger eqn to account for fermion/boson effects

I have been playing with an implementation of Visscher's explicit method for solving the time dependent Schrodinger equation (Are there simple ways to numerically solve the time-dependent ...
0
votes
1answer
415 views

a circular plot from a vector which represents the temperature along the radius surface, which is the same for every radius

I have calculated the temperature of the section of a cylinder, which is subjected to a heat flow on its upper surface. Getting the temperature distribution in the 2D section. As shown in the ...
1
vote
1answer
59 views

Integer simplification of irrational inequality

I'm doing work in computational geometry where the robustness of the algorithm is important. On two separate occasions now have I come across a scenario where I compare the numerical size of two ...
5
votes
1answer
112 views

What spline functions are used in Section 13.9 of “Numerical Recipes in C”?

I asked a similar question on MathSE but with more added fluff, but didn't really get any straight answers, so I figured I'd ask here. Computing Fourier coefficients of a function using the FFT is ...
0
votes
1answer
68 views

Finding roots without knowing much about the function

Consider solving numerically for roots: $( x_0, y_0): f(x_0, y_0) = 0, g(x_0, y_0) = 0$ where you only know that f, g continuously differentiable but the theoretical differentiation is not a ...
4
votes
1answer
310 views

Coupled nonlinear PDEs with time dependence on the RHS

I would like to numerically solve the following system of 2 coupled partial differential equations for the unknown functions $\psi_X(x,y,t)$ and $\psi_C(x,y,t)$: $\partial_t \psi_X = -i\psi_C - ...
2
votes
0answers
585 views

Self-consistent numerical solution of a set of equations

I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- $$\left(\begin{array}{cc} ...
5
votes
2answers
132 views

Convergence issues for a non-linear system

I have a nasty system of coupled integral equations, which I managed to discretize and recast a non-linear system, i.e. something like: $$ \vec{w} = F \left( \vec{w} \right) \hspace{32pt} w \in ...
6
votes
2answers
286 views

Is there any numerical reason for not using repeated multiplication instead of integer powers?

I recently discovered that, in MATLAB 2013b at least, it is significantly faster to do repeated multiplication rather than integer powers. That is, ...
23
votes
5answers
708 views

Are there simple ways to numerically solve the time-dependent Schödinger equation?

I would like to run some simple simulations of scattering of wavepackets off of simple potentials in one dimension. Are there simple ways to numerically solve the one-dimensional TDSE for a single ...
7
votes
1answer
154 views

Implementation of convection scheme given by normalized variable diagram

In finite difference and finite volume methods, convection schemes (upwind, central, quick, ...) are usually shown in a normalized variable diagram. The diagram gives the normalized face variable as a ...
2
votes
1answer
120 views

Monte Carlo normalization of a wave function

I would like to normalize a quantum mechanical multi-particle wave function numerically, and since the result is a multidimensional integral I thought Monte Carlo methods might be appropriate. So, I'm ...
2
votes
1answer
115 views

Question about extending Tikhonov regularization

I know that the Tikhonov regularization of a linear system has an analytical solution given by: \begin{equation} \hat{\mathbf{x}} = \mathrm{arg\;min}\left( \left| \mathbf{Ax} - \mathbf{b} \right|^{2} ...
2
votes
2answers
89 views

Advice on the regularisation of a linear problem

I'm numerically inverting an integral transform using a method suggested by a scicomp user from an earlier question. The problem is as follows: I wish to estimate $f(x)$ for a given $F(y)$, both of ...
2
votes
0answers
22 views

Approximate convolution of independent Beta variates?

Is there a way to approximate the convolution of Beta variables? Specifically, I am trying to find an approximation to $g(x_0)$: $$g(x_0) = \int \delta(x_0-\sum_{i=1}^{n} a_i x_i) \prod_{i=1}^{n} ...