Arjuna Ranasinghe

On a Linearizing Transformation For Burgers Equation

The initial/boundary value problem on the semi-infinite interval and on a finite interval for the burgers equation

u_t = u_xx + 2u_xu

is solved using a stream function φ and a linearizing transformation

w = exp(φ).

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 φ in our computations. Further, our computations are free of approximations.