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

learn more… | top users | synonyms

0
votes
0answers
38 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
172 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
80 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
126 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
83 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
80 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
63 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
600 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
39 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
150 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
57 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
99 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
65 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
276 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 - ...
1
vote
0answers
327 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
130 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
244 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, ...
22
votes
5answers
398 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 ...
6
votes
0answers
102 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
110 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
110 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
82 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} ...
5
votes
3answers
169 views

What are projection methods

Quoting from Solenthaler et. al. Predictive-Corrective Incompressible SPH (ACM Transactions on Graphics, Vol. 28, No. 3, Article 40, Publication date: August 2009) (PDF link here) These ...
2
votes
1answer
64 views

Methods to solve this equation on finite fields?

Is there any analytical (exact, closed-form solution) or numerical method to solve an equation such as $p(x) = r^x$ where $p(x)$ is a polynomial whose coefficients are drawn from a finite field, ...
5
votes
3answers
218 views

A clean way to compute exp(-1/x^2) near x=0 in C?

I am looking for a clean way to compute preciseley, when $x$ is very close to zero: $$\exp(-1/x^2)$$ using C. What is the best way (speed, precision, etc.) ?
4
votes
3answers
186 views

Is there a general framework for solving PDEs on uniform grid in parallel

Hej, I want to simulate a partial differential equation (a modified Cahn-Hilliard equation, but the details do not matter much. The questions also applies to the diffusion equation). I'm looking for ...
3
votes
3answers
155 views

Numerical scheme with energy conservation?

I have a set of equations to integrate something in time $t$. At each time step I compute a scalar field $\phi(t)$ and a potential $V(\phi)$. I should also control the conservation of energy with an ...
2
votes
1answer
236 views

Split operator FFT quantum dynamics for a harmonic oscillator

I would like to do a numerical quantum dynamics of a displaced gaussian in harmonic oscillator using split-operator method (see bottom of these notes by Hal Evans for the algorithm). I have a problem ...
5
votes
1answer
114 views

Energy Conservation

I'm working on a time integration scheme for my research. As a result, I have come across an interesting phenomenon. Somehow, the total energy of the scheme oscillates. At any given time the total ...
4
votes
0answers
77 views

Why do I get “estimated error” -1.#IND when doing BICGSTAB linear solver using ILUT perconditioner in eigen

I'm using Eigen (a C++ library for numerical linear algebra) to solve a linear equation with the the bi-conjugate gradient BICGSTAB algorithm with Incomplete LU preconditioner. However, the result ...
5
votes
1answer
643 views

generalized eigenvalue problem

I need to solve a real generalized eigenvalue problem $Ax= \lambda Bx(*)$ A and B are calculated from equations below: $$A=\sum_{i,j=1}^{N}W_{ij}(K_{i}-K_{j})\beta\beta^{T}(K_{i}-K_{j})^{T}$$ ...
4
votes
1answer
103 views

Boundary value technique for heat equation

My heat equation is $$ \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2}, \quad x \in [0,1], \quad t \in (0,0.1] $$ with initial condition $u(x,0)=\sin(\pi x)$ and homogeneous ...
8
votes
2answers
352 views

Is the maximum/minimum principle of the heat equation maintained by the Crank-Nicolson discretization?

I'm using the Crank-Nicolson finite difference scheme to solve a 1D heat equation. I'm wondering if the maximum/minimum principle of the heat equation (i.e. that the maximum/minimum occurs at the ...
12
votes
2answers
2k views

What is pseudo time-stepping?

While reading some literature on PDE solvers I came across the term pseudo time-stepping today. It seems to be a common term, however I failed to find a good definition or an introductionary article ...
21
votes
3answers
508 views

How does one test a numerical ODE solver implementation?

I'm about to start working on a software library of numerical ODE solvers, and I'm struggling with how to formulate tests for the solver implementations. My ambition is that the library, eventually, ...
3
votes
3answers
638 views

Can anyone recommend a library in C++ which has the most efficiency in doing sparse matrix operations under Windows system

I have download sparselib++, but it seems that it can't be complied in Windows, only in Unix, I don't know. So can anyone recommend some which can be used in Visual Studio 2010? I want to do a large ...
4
votes
2answers
129 views

How does longer simulation time affect simulation results?

I have a transient flow and solute transport simulation running using a fortran code. The final solution time is 1 day. I need the output of hydraulic head for the output time of 0.5 day. I want to ...
7
votes
3answers
579 views

manufactured solutions for incompressible Navier-Stokes — how to find divergence-free velocity fields?

In the method of manufactured solutions (MMS) one postulates an exact solution, substitutes it in the equations and calculates the corresponding source term. The solution is then used for code ...
4
votes
2answers
152 views

Problem Condition and Algorithm Stability

Consider 2 mathematical problems: $$ f_1(x) = a - x \\ f_2(x) = e^x -1 $$ The condition number for a function is defined as follows: $$ k(f) = \left| x \cdot \frac{f'}{f} \right| $$ Lets analyze ...
7
votes
1answer
185 views

Method selection for numeric quadrature

Several families of methods exist for numeric quadrature. If I have a specific class of integrands how do I select the ideal method? What are the relevant questions to ask both about the integrand ...
17
votes
2answers
417 views

Why do equi-spaced points behave badly?

Description of experiment: In Lagrange interpolation, the exact equation is sampled at $N$ points (polynomial order $N - 1$) and it is interpolated at 101 points. Here $N$ is varied from 2 to 64. ...
12
votes
3answers
430 views

Numeric Quadrature with Derivatives

Most numerical methods for quadrature treat the integrand as a black-box function. What if we have more information? In particular, what benefit, if any, can we derive from knowing the first few ...
7
votes
0answers
142 views

How does positivity preservation fit into the implication chain from monotone to monotonicity preserving?

I know from "Numerical Methods for Conservation Laws" by Randall J. LeVeque that there is an implication chain of properties of methods for conservation laws: monotone $\Rightarrow$ $L^1$-contractive ...
8
votes
1answer
352 views

Higher order Lax-Wendroff type scheme?

Suppose we want to solve a hyperbolic conservation law $u_t+f(u)_x=0$. I really like to use Lax-Wendroff, which reads $u_j^{n+1} = u_j^n -\frac{\Delta t}{\Delta ...
6
votes
5answers
242 views

Evaluate the sum

I want to evaluate the sum $$\sum_{k=1}^\infty \left(\frac{i+1}{\sqrt{2}}\right)^k\cdot k^{-\alpha}$$ where $i=\sqrt{-1}$ and $\alpha\in[\frac{3}{4},1]$ with 8 digits accuracy. If I am willing to ...
3
votes
0answers
57 views

Dissipation and symplectic manifolds

I'm working on an API for simulation of port-Hamiltonian systems. As far as I understand it, a Hamiltonian system is symplectic if it is power conserving, and so including resistive elements would ...
1
vote
2answers
359 views

complexity of flux limiter techniques

My question is not related to any particular problem, rather, I am looking at the equations of the form $$u_t+c(t,x)u_x=0$$ and attempt to solve it numerically. According to ...
1
vote
1answer
269 views

How easy is it to combine symbolic and numeric computation in Matlab?

CS Beta people: I have been doing some multiple integrals with a combination of symbolic and numerical integration (because symbolic answers have not always been possible). I have been using ...
5
votes
1answer
127 views

Periodic BC for Multigrid in MD

I know that this question might be very specific and maybe nobody will know the answer, but this is probably the only community where I could find an answer: So, as part of my master's project, I am ...