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Computational Science : Recent Questions and Answers (Page 9)

Find answers to your questions about Computational Science or help others by answering their Computational Science questions.

Discretization formula for a system of two differential equations. "Solution to one of these is the initial condition of the other". In which sense?

Consider the following stochastic differential equationbegin{equation}dy=left(A-left(A+Bright)yright)dt+Csqrt{yleft(1-yright)}dWtag{1}end{equation}where $A$, $B$ and $C$ are parameters and $dW$ is a Wiener increment.Equation $(1)$...

Asked on 08/29/2021

0 answer

How avoid square shape with Laplacian operator in reaction diffusion calculations?

I have used different variants of the Laplacian operator (div grad) using 4, 8, 12, 20 and 24 of the closest points. I get problems due to the chosen coordinate...

Asked on 08/28/2021

1 answer

traction boundary conditions in elasticity

I have a question about implementing traction boundary conditions in 2D and 3D linear elasticity. Consider the picture above. I...

Asked on 08/28/2021

1 answer

What's the simplest way to graph a 2d array generated in C++ using Windows 7?

This was so much easier in Python (so much so that I'm considering going back to matplotlib for data analysis). But really, trying to figure out ROOT and Boost...

Asked on 08/27/2021 by Hair of Slytherin

4 answer

How is the final result calculated in RK-Dopri(4,5)?

I have found a toy implementation of RK-Dopri(4,5), written in Python. I am concerned however, about line 118:y = y + h *...

Asked on 08/26/2021

1 answer

Optimization of expensive model with many parameters

I have a physical model which takes $sim50$ parameters and gives $sim2000$ outputs taking tens of minutes to run. I need to optimize these parameters to give outputs...

Asked on 08/26/2021

2 answer

Flux sign and face normal confusion in finite volume method

I implemented a solver for the 2D steady-state heat equation (without heat generation and homogeneous material) $nabla. (knabla T) = 0$, using finite volume method, however, I am having...

Asked on 08/24/2021

3 answer

Computation of a functional for large values

Consider the following function : $$f(x) = sin^2(frac{πGamma(x)}{2x})$$ Now consider the following functional :$$I(x)=int_0^infty frac{f(x + iy) − f(x − iy)}{e^{2πy}-1} dy$$I need values for of $I(x)$...

Asked on 08/22/2021

0 answer

Which scheme for inhomogeneous convection-diffusion equation with highly variable coefficients?

I have a 1D convection-diffusion equation $sigma_t = a(x,t) sigma_{xx}+b(x,t)sigma_x+f(x,t)$ defined on the unit interval, with nonzero Neumann boundary conditions at both ends. It should be noted that the...

Asked on 08/22/2021 by kieransquared

1 answer

interface value on the error equation

https://www.jstor.org/stable/pdf/2157482.pdf, here I have a problem in last equation of (2.6) in section (2.1). When they are considering error equation on the interface $Gamma$ they get...

Asked on 08/22/2021

1 answer

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