In the previous two problems, let $c = 1$ . Thesolution for u along the line $t = 0.5$ at the mesh points is Select all that apply.
A) $u _ { 11 } = 0$
B) $u _ { 11 } = 20 / 9$
C) $u _ { 11 } = 30 / 9$
D) $u _ { 21 } = 26 / 9$
E) $u _ { 21 } = 32 / 9$

Question

Quizplus · Accepted Answer

The solution for u along the line $t = 0.5$ at the mesh points is given by:$$u_{ij} = \frac{1}{4}(u_{i-1,j} + u_{i+1,j} + u_{i,j-1} + u_{i,j+1})$$At the mesh point $(1,1)$, we have:$$u_{11} = \frac{1}{4}(u_{01} + u_{21} + u_{10} + u_{12}) = \frac{1}{4}(0 + 20/9 + 0 + 30/9) = 20/9$$At the mesh point $(2,1)$, we have:$$u_{21} = \frac{1}{4}(u_{11} + u_{31} + u_{20} + u_{22}) = \frac{1}{4}(20/9 + 26/9 + 0 + 32/9) = 26/9$$

In the Previous Two Problems, Let c=1c = 1c=1 Thesolution for U Along the Line

In the Previous Two Problems, Let $c = 1$ Thesolution for U Along the Line