Differential Equations Ordinary and Partial Differential Equations Math Forum

 November 13th, 2016, 04:40 AM #1 Newbie   Joined: Nov 2016 From: Italy Posts: 1 Thanks: 0 Solve PDE - elliptic equation Hi, I have to solve this PDE: $U_{xx} +U_ {xy}+U_{yy}+sin(u)=12*(x^2+y^2)+sin(x^2+y^2)$ The domain is $U(0, y)=y^4; U(1, y)=1+y^4; U(x, 0)=x^4; U(x, 1)=1+x^4;$ First of all I think that I change the equations in canonical form, I do this with: ${ ( eta=((3)^(1/2)x/2 ),( ξ=y-(1/2)x ):}$ This is quite easy. The problem is the domain: How can I transform in the new coordinates? I need a domain that is rectangular: I want to solve the equation with Jacobi iterative method. Thanks Tags elliptic, equation, pde, solve Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Singularity Calculus 1 December 12th, 2012 09:30 AM mathbalarka Calculus 1 June 12th, 2012 01:27 PM mathbalarka Algebra 4 April 5th, 2012 04:39 PM wannabe1 Number Theory 0 March 19th, 2012 09:35 AM Kolobok Differential Equations 0 May 10th, 2010 12:09 AM

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