A compilation and some numerical results of numerical methods for the solution of a special class of second-order differential equations

Recent method developments for the numerical solution of initial value problems of the form y" = f(x, y) are investigated in this thesis. Since text books on the numerical solution of differential equations contain little or no information on methods produced in the last ten years, the content of major journal articles is surveyed. The approaches that authors have used to develop new methods are discussed. Since a large portion of the literature pertains to P-stable methods, results of numerical experiments conducted for many P-stable methods are reported and some conclusions are drawn. A proposed stability criterion for y" = f(x, y) is also briefly examined.