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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 March 31st, 2019, 08:43 PM #1 Newbie   Joined: Mar 2019 From: Russia Posts: 2 Thanks: 0 Partial Differential Equation Help please, I need to solve this differential equation $\displaystyle x\frac{\partial^2 U}{\partial x^2}+y\frac{\partial^2 U}{\partial y^2}=aU$ in Matlab (where "a" is a constant parameter, it can be taken by any), I wanted to use the Partial Differential Equation Toolbox, but I ran into a problem, the elliptic equation in this Toolbox is represented in a vector form, namely -div(c*grad(u))+a*u=f. Please help me convert my equation to this form and tell me how it can be done or at least name the sources of information from which I can learn this knowledge. I really need to solve this equation in Matlab,so please tell me how it can be done. April 1st, 2019, 07:20 PM #2 Senior Member   Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 Math Focus: Dynamical systems, analytic function theory, numerics You probably can't convert your equation to this form. Your equation is nonlinear and second equation you have written is linear. In the unlikely even that it is possible to convert it then it will be some nonlinear change of coordinates which is non-obvious. Most importantly, there is no canonical or algorithmic way to change your equation to this form. Thanks from topsquark April 2nd, 2019, 06:20 AM #3 Newbie   Joined: Mar 2019 From: Russia Posts: 2 Thanks: 0 Thanks for the answer, in that case could you tell me how to solve it in Matlab? Is there any way to solve this equation using built-in matlab methods, without algorithm processing and writing code from scratch? April 2nd, 2019, 02:19 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2202 Your equation is linear; I don't know why SDK thought it isn't. Thanks from SDK April 2nd, 2019, 10:59 PM   #5
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Quote:
 Originally Posted by skipjack Your equation is linear; I don't know why SDK thought it isn't.
Thanks for noticing this. I misread the equation and thought $y$ was the solution variable. Tags differential, equation, matlab, partial, pde 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 harley05 Differential Equations 2 May 7th, 2015 01:37 PM mona123 Differential Equations 1 January 21st, 2015 03:21 PM mathbalarka Differential Equations 0 September 19th, 2012 09:14 PM WananoMath Differential Equations 1 February 3rd, 2007 08:44 PM WananoMath Differential Equations 7 February 1st, 2007 10:42 AM

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