A class of numerical methods for autonomous initial value problems

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Flavius Olimpiu Pătrulescu


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.

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initial value problem; stability region; convergence order; local truncation error