Superstable single-step methods for second-order initial-value problems

Abstract

Single-step methods of orders four and six are derived for the numerical integration of general second-order initial-value problems y″ = f( x, y, y′), y( x 0) = y 0, y′( x 0) = y′ 0. The methods when applied to the test equation y″ + 2α y′ + β 2 y = 0, α, β ⩾ 0, α + β > 0 are superstable in the sense of Chawla [1] with the exception of a finite number of isolated values of β h. Numerical results demonstrate the efficiency of the methods.