Unconventional schemes for a class of ordinary differential equations - with applications to the Korteweg-de Vries equation (Q1368649)

The authors describe a class of methods they call reflexive which when applied to a system of differential equations \(y'=f(y)\), where \(f(y)\) is quadratic in \(y\), is equivalent to one step of a Newton iteration and hence second order. They propose a systematic and easily implemented scheme and apply it to the solution of the Korteweg-de Vries equation.