- #1
sigh1342
- 31
- 0
For possion equation $$u_{xx}+u_{yy}=f$$
I know the general five point scheme is in the form
$$a_{1}U_{i,j-1}+a_{2}U_{i-1,j}+a_{3}U_{i,j}+a_{4}U_{i+1,j}+a_{5}U_{i,j+1}=f_{i,j}$$
But , is there have the form
$$a_{1}U_{i-1,j-1}+a_{2}U_{i-1,j+1}+a_{3}U_{i,j}+a_{4}U_{i+1,j+1}+a_{5}U_{i+1,j-1}=f_{i,j}$$?
I know the general five point scheme is in the form
$$a_{1}U_{i,j-1}+a_{2}U_{i-1,j}+a_{3}U_{i,j}+a_{4}U_{i+1,j}+a_{5}U_{i,j+1}=f_{i,j}$$
But , is there have the form
$$a_{1}U_{i-1,j-1}+a_{2}U_{i-1,j+1}+a_{3}U_{i,j}+a_{4}U_{i+1,j+1}+a_{5}U_{i+1,j-1}=f_{i,j}$$?