Questions tagged [parabolic-pde]

A partial differential equation that describes diffusion phenomena.

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Boundary Conditions for the given PDE

I'm working on the Black-Scholes equation, but I'm pretty new to financial modeling. Right now, I am trying to understand the Black-Scholes PDE. I understand that the Black-Scholes equation is given ...
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Heat Equation - PDE

I'm trying to model the Black-Scholes Equation (transformed into a heat equation) using method of lines in Python. The transformed formula is basically \begin{equation*} \frac{\partial u}{\partial ...
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Applying the method of lines to parabolic PDEs: references and software

Could you please advise some literature about the numerical method of lines (MOL) for parabolic PDEs? It is a method of solving PDEs with discretizing only by space but not by time. A system of ODEs ...
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Modeling First Order Parabolic PDE (Battery Storage Model)

I'm trying to solve the following first order parabolic partial differential equation, \begin{equation*} X \frac{\partial V}{ \partial Q} = -\frac{1}{2} \sigma^2 \frac{\partial^2 V}{\partial X^2} + ...
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How to recreate this result (from a book)?

The result I'm interested in is found within "Synchronization: A Universal Concept in Nonlinear Sciences" page $333$ figure $14.3$. The peculiar fragment is also provided at the end of this post. So ...
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Is there a good tutorial or textbook-like source on implementing ENO/WENO with limiters in one (and more than one) dimension?

I've inherited a finite volume code that does a second-order discretization of flux terms for a set of mixed parabolic-elliptic equations with discontinuous diffusion coefficients. The impression I ...
I want to numerically solve the non-linear diffusion equation: $$\frac{\partial}{\partial t} T(x,t)= \frac{\partial}{\partial x}\left(T^{5/2} \frac{\partial T}{\partial x} \right)$$ I want to use ...