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Spot the fish!

Statistics: Posted by katastrofa — Today, 12:15 am

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And thanks for reminding me, otherwise I wouldn't have known that he has a new book out. His previous, "Anger is an Energy," is one of my favourite autobiographies (along with David Niven, Paul O'Grady and PT Barnum, non-entertainer autobios are usually tedious I find).

Statistics: Posted by Paul — Today, 12:00 am

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Statistics: Posted by katastrofa — Yesterday, 11:55 pm

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Maybe it's within the ethical principles of this science nouveau.

In other photos and according to other models she was also a capuchin, black-footed ferret and titi.

Statistics: Posted by katastrofa — Yesterday, 11:52 pm

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Statistics: Posted by katastrofa — Yesterday, 11:37 pm

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On suggestion from JohnLeM.

Always good to start with a definition,thus avoiding other alternate mental models

https://www.cfd-online.com/Wiki/Monotone_scheme

Excellent !Always good to start with a definition,thus avoiding other alternate mental models

https://www.cfd-online.com/Wiki/Monotone_scheme

A first comment: we might wish to slightly modify this definition, because it does not seem to match finite difference schemes, that are the basic schemes one should study.

For instance consider a mesh of I points [$] x^1,...,x^I [$], denote a discretized function as a vector [$]u^n := (u^n_i \sim u(t^n,x^i))_i[$]. Considering a linear problem, after discretization, we often get a linear semi-group having form

[$] u^{n+1} = H(x^1,...,x^I) u^{n}[$], where [$]H(x^1,...,x^N)[$] is a matrix of size [$]I \times I[$]. Hence we should modify slightly the definition pointed out on cfd on line:

A scheme [$]v = H(u)[$], [$] H : \mathbb{R}^I \mapsto \mathbb{R}^I[$] is monotone if the Jacobian [$]\nabla H = \Big( \partial_{u^i} H_j(u) \Big)[$] is a positive matrix.

Let us test this view on the heat equation [$]\partial_t u = \Delta u[$] for a simple euler scheme [$]u^{n+1} = u^{n} + \delta_t \Delta^h u^n, \Delta^h[$] being your favorite discretization of the Laplacian, [$]\delta_t[$] a time step. The scheme is monotone provided that the matrix[$]I_d + \delta_t \Delta^h[$] is a positive matrix. If one takes for instance the classical difference scheme [$]\Delta^h = \frac{1}{\delta_x^2}(...,+1,-2,+1,...) [$] we get that the scheme is monotone if [$] \frac{\delta_t}{\delta_x^2} \le 1 [$], that is also the quite known CFL condition for the heat equation.

Statistics: Posted by JohnLeM — Yesterday, 8:28 pm

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https://www.irishcentral.com/news/major ... -237416911

I can see Annagassan looking across Dundalk Bay from my cottage.

The Annals of Ulster record that in 851, Danish Vikings (the Dubhgall) attempted to attack the Norwegian Viking (Fingall) settlement at Annagassan at the southern end of Dundalk Bay and were heavily defeated. The following year, Norwegian Vikings based in Scotland were sent to attack the Danes in Carlingford Lough but their expedition was unsuccessful.

a lot of in-fighting with ye Scandinaviers.

Statistics: Posted by Cuchulainn — Yesterday, 7:31 pm

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www.youtube.com/watch?v=_8mduTEvnU0

Statistics: Posted by Cuchulainn — Yesterday, 6:52 pm

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https://www.rte.ie/news/dublin/2020/092 ... dy-dublin/

The dig has also established that Vikings continued living at the Dubh Linn even after the more famous Wood Quay settlement was established a kilometre away.

Statistics: Posted by Cuchulainn — Yesterday, 6:17 pm

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Always good to start with a definition,thus avoiding other alternate mental models

https://www.cfd-online.com/Wiki/Monotone_scheme

Statistics: Posted by Cuchulainn — Yesterday, 5:53 pm

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[$] \frac{\Delta t}{(\Delta S)^2}<\frac12 [$]

Yes and no; only for the pure heat equation.

Here's the full analysis

https://www.lexifi.com/quant/possible-s ... equations/

We had also a number of discussions spread everywhere at Wilmott forums concerning monotone schemes, that are probably the best schemes for Finance applications. We should work this topic, I still feel uncomfortable here. Maybe a dedicated thread if someone is interested ?Yes and no; only for the pure heat equation.

Here's the full analysis

https://www.lexifi.com/quant/possible-s ... equations/

Statistics: Posted by JohnLeM — Yesterday, 5:37 pm

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Yes and no; only for the pure heat equation.

Here's the full analysis

https://www.lexifi.com/quant/possible-s ... equations/

Statistics: Posted by Cuchulainn — Yesterday, 4:51 pm

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I am still doing the same mistakes ever and ever :/There's no h in Nicolson.

Next time I'll send my cousin to sort you guys out!

Statistics: Posted by Cuchulainn — Yesterday, 4:35 pm

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