New L-stable method for numerical solutions of ordinary differential equations

Recently, Kondrat and Jacques [D.M. Kondrat, I.B. Jacques, Extended A-stable two-step methods for the numerical solution of ODEs, Int. J. Comput. Math. 42 (1992) 117–124], Bulut and Inc [H. Bulut, M. Inc, A two-step method for the numerical integration of stiff differential equations, Int. J. Comput. Math. 73 (2000) 333–340] have reported on an extended two-step fourth-order A-stable method. In this paper we describe a new class of stabilised fourth-order L-stable method. Numerical results are presented for three test problems.