I am using separation of variables and superposition to solve:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]u_{xx}+u_{yy}=0;

for (x,y) \in (0,L) [/tex] X [tex] (0,H)[/tex]

[tex]u(0,y)=f(y);

u(L,y)=0;

u(x,0)=g(x);

u(x,H)=0[/tex]

Is it correct to assume that I can write my solution as:

[tex]u=u_1+u_2[/tex]

Where:

[tex]u_1[/tex]

is the solution with BC

[tex]u(0,y)=0;

u(L,y)=0;

u(x,0)=g(x);

u(x,H)=0[/tex]

And:

[tex]u_2[/tex]

is the solution with BC

[tex]u(x,0)=0;

u(x,H)=0;

u(0,y)=f(y);

u(L,y)=0[/tex]

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# Homework Help: Laplace's Equation Solution in 2D

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