Solution of the Burgers equation on semiinfinite and finite intervals via a stream function
The initial-boundary-value problem on the semiinfinite interval and on a finite interval for the Burgers equation u"t = u"x"x + 2u"xu is solved using a stream [email protected] a linearizing transformation w = e^@f. The transformation reduces the equation to a heat equation with appropriate initial and homogeneous time-dependent linear boundary conditions. One advantage of this method is that we never need to find an explicit expression for @f in our computations.