THE ACCURATE ELEMENT METHOD FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

May 7, 2005

This book represents the further development of a previous one issued in 2001, “A new method for accurate solving of Ordinary Differential Equations”. Here the method has received a name: the Accurate Element Method (AEM). Though all times the ideas put forward in the book have been verified as being valid, the approach taken here is totally different, trying to be more “friendly” with the reader and avoiding some cumbersome calculations. The Accurate Element Method (AEM), which is based on a simple and non-sophisticated mathematical approach, introduces two new concepts: The Complete Transfer Relation (CTR) and the Concordant Functions (CF).

Numerous numerical experiments are presented which illustrate that all the problems connected to the integration of an ODE (Initial Value, Boundary Value, Eigenvalue problems) are solved by the Accurate Element Method in the same way, by using the same CTR and CF. The results are compared with those provided by other numerical methods, especially Runge-Kutta. A part of this book can be described as “Accurate Element Method versus Runge-Kutta“, where the reader may have some surprising revelations concerning the reliability and accuracy of the two methods.