## Abstract

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.

## Authors

Flavius **Patrulescu**

(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

## Keywords

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

## Cite this paper as

F. Pătrulescu, *A numerical method for the solution of an autonomous initial value problem*, Carpathian J. Math. vol. 28 (2012), pp. 289-296

## About this paper

##### Journal

Carpathian Journal of Mathematics

##### Publisher Name

North University of Baia Mare, Department of Mathematics and Computer Science, Baia Mare

##### Print ISSN

1584-2851

##### Online ISSN

1843-4401

## MR

3027258

## ZBL

1289.65153

## Google Scholar

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