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

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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 ...
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1answer
53 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
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1answer
85 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 ...
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1answer
63 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
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1answer
255 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 - ...
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0answers
219 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} ...
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2answers
127 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 ...
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228 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, ...
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4answers
246 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
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76 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
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1answer
101 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
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1answer
108 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} ...
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2answers
77 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 ...
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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
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3answers
154 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
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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
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3answers
214 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.) ?
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3answers
164 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 ...
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3answers
150 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
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1answer
191 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
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1answer
97 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 ...
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69 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
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1answer
587 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
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1answer
100 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 ...
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295 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 ...
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2answers
1k 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 ...
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432 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, ...
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3answers
508 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 ...
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2answers
128 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
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3answers
524 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 ...
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2answers
151 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 ...
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168 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 ...
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379 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
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364 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 ...
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139 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
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1answer
313 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 ...
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5answers
238 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 ...
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0answers
55 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 ...
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2answers
334 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 ...
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1answer
205 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
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1answer
107 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 ...
13
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1answer
431 views

can I trust this numerical triple integral from Matlab?

Computational Science people: I originally posted this question at Math Stack Exchange and someone commented that I might get "much better" answers here: I am a novice at numerical methods and ...
4
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2answers
181 views

Numerical simulation of particle in magnetic field

I'm interesting in numerically simulating (with my own code, not an off-the-shelf package) the motion of a single electrically charged particle in a magnetic field. The field will vary in time and ...
2
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0answers
65 views

How to compute the sum of a power series in a more robust way?

In order to compute the sum of a power series, we can use for loop, while loop or the analytic formula. I am wondering what is difference between those algorithms and how to improve the robustness of ...
1
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1answer
121 views

Discrete convolution

please can I ask a bit stupid question? Let say I need to solve an equation in a form $\frac{\partial X}{\partial t}=\sum_k M_k * X_{n-k}$ How can I do the discrete convolution numerically? I will say ...
4
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1answer
159 views

Numerical Methods for minimizing a Non-Differentiable Convex Function of Several Variables

I have a multi-variable convex continuous function which is not differentiable. I am interested to know about different numerical techniques, possibly also references to them, used for this. Read ...
14
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1answer
221 views

Does transforming $J_0(x)\to\int\cos(x\sin\theta)$ help with numerical integration?

I've heard anecdotally that when one is trying to numerically do an integral of the form $$\int_0^\infty f(x) J_0(x)\,\mathrm{d}x$$ with $f(x)$ smooth and well-behaved (e.g. not itself highly ...
3
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1answer
96 views

Introduction for (numerical) linear algebra of random variables

I am in search of an introduction into numerical linear algebra - or, at least, pure linear algebra - that treats the case when the input data are random variables. A typical application would be to ...
3
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1answer
567 views

cholesky factorization of block matrices

I have a block matrix (either 2x2 blocks or 3x3 blocks) which is the covariance matrix for a joint space of two or three multivariate normal variables. ie ...
3
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1answer
391 views

generating a non-uniform grid with Chebyshev discretization

I often see that it is common to put "more points" in the region of interest in the computational domain of the numerical method, i.e. use non-uniform grid. The proofs are usually done for the uniform ...