au 1. Consider the following nonlinear partial differential equation: ди ди tu = 0.1 where x e [0,1] at дх дх2 u(x,0) =

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au 1. Consider the following nonlinear partial differential equation: ди ди tu = 0.1 where x e [0,1] at дх дх2 u(x,0) = sin(rex); u(x = 0,0) = 0; u(x = 1,t) = 0 a. Use a second-order finite volume scheme with explicit time stepping. b. Use a second-order finite volume scheme with implicit time stepping and use the Newton- Raphson method to solve the coupled nonlinear equations. For both parts (a) and (b) clearly show your discretized equations for the interior cells and the boundary cells. Also, plot your solutions at t = 0.3, t = 0.5, t = 0.7, and t = 0.9 on one figure (but label the different times either directly or using a legend). i hani JE