Using a known interpolation formula we introduce a class of numerical methods for approximating the solutions of scalar initial value problems for first order differential equations, which can be identified as explicit Runge-Kutta methods. We determine bounds for the local truncation error and we also compare the convergence order and the stability region with those for explicit Runge-Kutta methods, which have convergence order equal with number of stages (i.e. with 2, 3 and 4 stages). The convergence order is only two, but our methods have a larger absolute stability region than the above mentioned methods. In the last section a numerical example is provided, and the obtained numerical approximation is compared with the corresponding exact solution.
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
initial value problem; stability region; convergence order; local truncation error
F. Pătrulescu, A numerical method for the solution of an autonomous initial value problem, Carpathian J. Math. vol. 28 (2012), pp. 289-296
Carpathian Journal of Mathematics
North University of Baia Mare, Department of Mathematics and Computer Science, Baia Mare