My Math Forum Poisson equation with three boundary conditions

 Differential Equations Ordinary and Partial Differential Equations Math Forum

November 20th, 2014, 05:55 AM   #1
Newbie

Joined: Nov 2014
From: London

Posts: 3
Thanks: 0

Poisson equation with three boundary conditions

I have the following 2D Poisson equation (which can also be transformed
to Laplace) defined on a triangular region (refer to plot):

\frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=C

with the following three boundary conditions:

\frac{\partial u}{\partial y}=0\,\,\,\,\,\,\,\mathrm{at}\, y=0

u=0\,\,\,\,\,\,\,\mathrm{at}\, y=ax+b

c\frac{\partial u}{\partial x}+d\frac{\partial u}{\partial y}=0\,\,\,\,\,\,\,\mathrm{at}\, y=ex+f

where $C,a,b,c,d,e,f$ are constants.

What is the easiest way to solve this problem (preferably analytically)?
Attached Images
 asd.PNG (4.6 KB, 0 views)

 Tags boundary, conditions, equation, poisson

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post gasper7 Real Analysis 4 May 23rd, 2013 11:55 PM Dodi Applied Math 0 February 10th, 2012 10:30 AM Dodi Calculus 0 February 10th, 2012 10:13 AM jacynty123 Calculus 0 May 21st, 2011 01:50 AM emirs Computer Science 0 July 9th, 2010 08:42 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top