- #1
neutrino2063
- 7
- 0
I am using separation of variables and superposition to solve:
[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]
[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]