Implementation of the Heronion mean (HeM) in the predictor corrector mode

Abstract

As is known, one of the most important and famous methods for solving initial value problems are the Runge Kutta methods. As the results of developing the computers and processors, now some of the old methods become not appropriate with parallel computers, so, here we introduce a new method suitable for the current generations of computers.

Subject Classification:

• Primary 11H60
• Secondary 26A24

Keywords:

• Initial value problems
• Heronion mean
• Predictor corrector method
• The stability