In this paper we introduce a class of explicit numerical methods for approximating the solutions of scalar initial value problems for first order differential equations, using a nonlinear interpolation formula. We show that the methods generated in this way can be identified as explicit Runge-Kutta methods and we analyze some particular cases. Finally, numerical examples are provided.
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
initial value problem; stability region; convergence order; local truncation error
F. Pătrulescu, A class of numerical methods for autonomous initial value problems, Rev. Anal. Numer. Theor. Approx., vol. 41, no. 1 (2012), pp. 82-92
Publishing House of the Romanian Academy (Editura Academiei Române), Cluj-Napoca