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MTH418/518 HW 6.Z (10 points) due 3/18 Use the finite difference method to solve "Burger's equation" with periodic boundary conditions: u 2u u = k 2...

Partial differential equations help please

MTH418/518 HW 6.3.Z (10 points) due 3/18 Use the finite difference method to solve “Burger’s equation” with periodic boundary conditions: ) ( ) 0 , ( 0 ) , ( ) , 0 ( 2 2 x f x u t L u t u x u u x u k t u = = = = (a) (5 pts) Derive the appropriate finite difference equations for this problem using forward difference for du/dt and center difference for the x derivatives. (b) (5 pts) Implement your finite difference equations in Maple. Use k=0.5, L=10, N=20 and f(x) = evalf(sin(Pi*x/L)). Choose T large enough to show the long-time behavior of the solution. Choose dt small enough so that the calculation is stable. Turn in a printout of your Maple code that includes plots of the solution at t=0, t=5, t=10, t=20.
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