Numerical solution of Burgers' equation by the Sobolev gradient method

Burgers' equation is solved numerically with Sobolev gradient methods. A comparison is shown with other numerical schemes presented in this journal, such as modified Adomian method (MAM) [1] and by a variational method (VM) which is based on the method of discretization in time [2]. It is shown that the Sobolev gradient methods are highly efficient while at the same time retaining the simplicity of steepest descent algorithms.