Boundary conditions in the linear difference equations system
– ui–1,j – ui,j–1 + 4ui,j – ui,j+1 – ui+1,j = 0 for i=0,…,m-1, j=0,…,n-1
? Boundary condition are used in the equations with i=0, i=m-1, j=0, j=n-1:
i=0, j=0 ? +4ui,j –ui,j+1 –ui+1,j = u–1,0 + u0,–1
i=0, 0<j<n–1 ? –ui,j–1 +4ui,j –ui,j+1 –ui+1,j = u–1,j
i=0, j=n–1 ? –ui,j–1 +4ui,j –ui+1,j = u–1,n–1 + u0,n
0<i<m–1, j=0 ? –ui–1,j +4ui,j –ui,j+1 –ui+1,j = ui,–1
0<i<m–1, 0<j<n–1 ? –ui–1,j –ui,j–1 +4ui,j –ui,j+1 –ui+1,j = 0
0<i<m–1, j=n–1 ? –ui–1,j –ui,j–1 +4ui,j –ui+1,j = ui,n
i=m–1, j=0 ? –ui–1,j +4ui,j –ui,j+1 = um,0 + um–1,–1
i=m–1, 0<j<n–1 ? –ui–1,j –ui,j–1 +4ui,j –ui,j+1 = um,j
i=m–1, j=n–1 ? –ui–1,j –ui,j–1 +4ui,j = um, n–1 + um–1,n