# Questions tagged [numerics]

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### 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 ...
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### 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 ...
2answers
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### 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. ...
0answers
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### 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 ...
1answer
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### 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 ...
2answers
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### 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. ...
1answer
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### 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 ...
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### 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) ...
1answer
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### 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 ...
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### 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, tau to z, tau. Since the integrand diverges at z=0.9, ...
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### 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: \...
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### 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 ...
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### 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 ...
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### 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 ...
1answer
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### 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 ...
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### How to implement adaptive step size Runge-Kutta Cash-Karp?

Trying to implement an adaptive step size Runge-Kutta Cash-Karp but failing with this error: ...