# Questions tagged [numerics]

The tag has no usage guidance.

688 questions
Filter by
Sorted by
Tagged with
10 views

### Numerically estimating expected value of f(x) when x is normally distributed

I need to estimate $$\mathbb{E}_x[f_i(x)] = \int_{\mathbb{R}^n} f_i(x) p(x) dx$$ for many functions $f_i(x)$, where $p(x)$ is the density of a normal distribution. The evaluation of all the ...
17 views

### Evaluate Nth root of a rational to a correctly rounded float

Excuse my lack of vocabulary for I have no formal training in this field, which is also why I ask this question - it may be trivial or it may be impossible. I want to evaluate an expression in the ...
236 views

### Boundary conditions for streamlines in enclosed flow

I am trying to solve Lid driven square cavity flow problem of Stokes equation using finite element method. I have boundary conditions for velocity as zeros on every boundary but u=1 on top boundary. ...
23 views

### How to compute the following Crank-Nicolson scheme for the viscous Burgers' Equation?

I am attempting to replicate results from this article. I'm not sure why but my results are wrong. Is anyone able to spot my mistake? I've included my code (in R) below. The Thomas algorithm was ...
527 views

3k views

### Scientific computing vs numerical analysis

I'm a double major in computer science and mathematics. I love both subjects. I'm thinking in taking a graduate career, perhaps in scientific computing. What's the real difference between scientific ...
489 views

### Solving PDE with spatial and temporal derivatives on left hand side

I wish to solve an equation of the form, $$\frac{\partial}{\partial t} \left( \frac{\partial \phi}{\partial x} \right) = -\frac{\partial}{\partial x}(\mathcal{F})$$ for the variable $\phi$ (e.g. ...
185 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 ...
58 views

### How to use Wolfe-Powell step-size control in quasi-Newton method?

I'm trying to find the minimum of a function using the quasi-Newton method with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. But I want to change the following implementation, so that: 1) ...
88 views

### Going back in time in an initial value problem

Consider an initial value problem (IVP) $y'=f(t,y)$ with the initial value given by $y(t=0) = 0$. If I need to find $y(t^*)$, hence finding the path for $y$ in $t \in [0,t^*]$ and $t^*<0$; is the ...
72 views

79 views

### How to : numerical integration by quadrature in C language / remove NaN

What I wanna solve it the problem following ( by quadrature method ) I want to get two arrays of data ( z & tau ) from z[0], tau[0] to z[2249], tau[2249]. Since the integrand diverges at z=0.9, ...
57 views

82 views

### Dirichlet to Neumann Operator

EDIT: I am trying to specify my Question. Also I am not going to clearify which spaces I use, because I am only interested in the basic idea. I am looking at a standard elliptic second order PDE: \...
36 views

### How to determine the order of convergence of the Euler-Maruyama method?

This question is originally posted in Quant.StackExchange but has been unanswered for some time so I ask in here. To make this simple let us consider the Geometric Brownian Motions (GBM). My ...
257 views

466 views

### Proper boundary conditions for potential flow around cylinder

I am computing the stationary, incompressible, inviscid and irrotational flow around a circular cylinder using a discretization in general coordinates. I derived a PDE and proper boundary conditions ...
41 views

### Singular Spectrum Analysis Explanation

I need you to help me understand the Singular Spectrum Analysis algorithm. I already read a lot of articles about the subject but they never answered my questions like what is the mathematical reason ...
2k views

### How to Run MPI-3.0 in shared memory mode like OpenMP

I am parallelizing code to numerically solve a 5 Dimensional population balance model. Currently I have a very good MPICH2 parallelized code in FORTRAN but as we increase parameter values the arrays ...