A note on variational-iterative schemes applied to Burgers' equation (Q1063403)

This paper applies a nonlinear variational-iterative method to the steady state version of Burgers' equation \(u(du/dx)=v(d^ 2u/dx^ 2),\quad x\geq 0\) where \(u(0)=0\), \(u(\infty)=-2v\) and v is a parameter. The variational method was introduced by the reviewer and \textit{A. J. Perks} [J. Phys. A 14, 797-808 (1981; Zbl 0463.49045)]. The novel aspect of the paper is an algorithm for choosing the trial functions to obtain a fast convergence rate.