# Search Results

Results tagged with Search options user 3691
14 results

Partial differential equations (PDEs) are equations that relate the partial derivatives of a function of more than one variable. This tag is intended for questions on modeling phenomena with PDEs, solving PDEs, and other related aspects.

It's a bit easier to see if you write your equation in the a semi-discretised system of the form $u^{\prime}(t) = F(u(t))$ and with the application of the $\theta$-method and approximating \$u^{\prime} …
answered Sep 11 '15 by boyfarrell
I am not very familiar with the common discretization schemes for PDEs. I know that Crank-Nicolson is popular scheme for discretizing the diffusion equation. Is also a good choice for the advection te …
asked Feb 28 '13 by boyfarrell
This might be a naive question, but when applying a implicit discretization to a PDE with a source term, should the source be averaged in time? For example if we take the diffusion equation with a …
asked May 29 '13 by boyfarrell
Starting with the advection equation is conservative form, $$\frac{\partial u}{\partial t} = -\frac{\partial (\boldsymbol{v} u)}{\partial x} + s(x,t)$$ The Crank-Nicolson method consists of a time …
answered May 28 '13 by boyfarrell
I wish to solve a coupled system of non-linear equation of this form, $$u_t = -(\mathcal{F})_x + f(x,u,w) \\ w_t = \mathcal{F} + g(x,u,w)$$ by stepping the equations forward in time. The first eq …
asked Jul 10 '13 by boyfarrell
(I realised the issue, after having a discussion offline). The answer is yes, and the equations are correct. The error is in assuming that the electron and hole densities should remain constant when …
answered Mar 18 '13 by boyfarrell
I am trying to understand an extra terms that appears when I derive the drift-diffusion equations for semiconductors. The extra term (see below) comes from applying the chain rule to the advection ter …
asked Mar 18 '13 by boyfarrell
Say we have a discretised a coupled nonlinear system of two PDEs to give a system of ODEs which approximates the original system, $$\frac{\partial u}{\partial t} = F_1(t,\boldsymbol{u,v}) \\ \frac{ … asked Sep 25 '13 by boyfarrell 1answer I don't understand the different behaviour of the advection-diffusion equation when I apply different boundary conditions. My motivation is the simulation of a real physical quantity (particle density … asked Mar 5 '13 by boyfarrell 3answers Following on from my previous equation I'm would like to apply open boundary condition to the advection-diffusion equation (with reaction term),$$ \frac{\partial \phi}{\partial t} = \frac{\partial}{ …