[math]\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0[/math]
[math]0 < x < 1, \ \ \ \ \ 0 < y < 2[/math]
[math]u(x,0) = x, \ \ \ \ \ u(x,2) = x^2[/math]
[math]u(0,y) = y, \ \ \ \ \ u(1,y) = y^2[/math]
This is a Laplace partial differential equation.
I don't know how to solve this problem. I looked for similar problems in the book, but did not find. I also looked for similar problems in the web, but did not find.
A very important note: If you think that this is an easy problem, don't underestimate my skills. I have solved the Airy Equation before from scratch.
[math]0 < x < 1, \ \ \ \ \ 0 < y < 2[/math]
[math]u(x,0) = x, \ \ \ \ \ u(x,2) = x^2[/math]
[math]u(0,y) = y, \ \ \ \ \ u(1,y) = y^2[/math]
This is a Laplace partial differential equation.
I don't know how to solve this problem. I looked for similar problems in the book, but did not find. I also looked for similar problems in the web, but did not find.
A very important note: If you think that this is an easy problem, don't underestimate my skills. I have solved the Airy Equation before from scratch.