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March 31st, 2019, 08:43 PM   #1
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Question 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.
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April 1st, 2019, 07:20 PM   #2
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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.
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April 2nd, 2019, 06:20 AM   #3
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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?
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April 2nd, 2019, 02:19 PM   #4
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Your equation is linear; I don't know why SDK thought it isn't.
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April 2nd, 2019, 10:59 PM   #5
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Quote:
Originally Posted by skipjack View Post
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.
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