Problem 3 (2 points)
For u(x,t) defined on the domain of 0<=x<=2pi and t>=0, solve the PDE,
(delu)/(delt)=(del^(2)u)/(delx^(2))+4t(del^(3)u)/(delx^(3))+t(del^(5)u)/(delx^(5))+u
with periodic boundary conditions in the x-direction, and the boundary condition in the
t-direction given as
u(x,0)=1+sin(x)+cos(2x).
Problem 3 (2 points) For u(x, t) defined on the domain of 0 x 2 and t 0, solve the PDE,
du a2u te ax2
03u a5u dx3 ax5 +u
with periodic boundary conditions in the x-direction, and the boundary condition in the t-direction given as
u(x, 0) = 1 + sin(x) + cos(2x)
