Verify coupling of the linear algebraic equations of the system (3.42)-(3.44) by writing the discretization formula for the interior grid points \(\left(x_{i}, t^{n}\right),\left(x_{i+1}, t^{n}\right),\left(x_{i}, t^{n-1}\right)\) and the points \(\left(x_{0}, t^{n}\right)\) and \(\left(x_{1}, t^{n}\right)\) near the boundary.

Transcribed Image Text:

u+1 = u + a At (Ax)2(-1-2+u+1)