Three-and four-derivative Hermite-Birkhoff-Obrechkoff solvers for stiff ODE

Abstract

Three- and four-derivative k-step Hermite-Birkhoff-Obrechkoff (HBO) methods are constructed for solving stiff systems of first-order differential equations of the form y'= f(t,y), y(t0) = y0. These methods use higher derivatives of the solution y as in Obrechkoff methods. We compute their regions of absolute stability and show the three- and four-derivative HBO are A( 𝜶)-stable with 𝜶 > 71 ° and 𝜶 > 78 ° respectively. We conduct numerical tests and show that our new methods are more efficient than several existing well-known methods.