Question: please help me...... Numerical methods to PDES: Problem Sheet 11 equation Consider the advection / Ut = -Ux, 9 (x, t) E (0,1) (0,T], u(0,t)

please help me...... Numerical methods to PDES:

please help me......

Numerical methods to PDES: Problem Sheet 11 equation Consider the advection / Ut = -Ux, 9 (x, t) E (0,1) (0,T], u(0,t) = 0 for te (0,T] | u(x,0) = g(x), X [0,1], x (1) where g(x) = 0, 0 [0, 0.2), 1, x (0.2, 0.4], 0, x (0.4, 1] , (2) Use Lax-Friedrichs method to find approximations to the above problem at different times. Use 40 uniformly distributed nodes to partition the domain. Provide the plots of the initial condition and approximations at time T=0.01, 0.2, 0.4, 0.6

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