Solution of an Initial Value Problemin Ordinary Differential Equations Using the Quadrature Algorithm Based on the Heronian Mean

Abstract

Over the years, the Quadrature Algorithm as a method of solving initial value problems in ordinary differential equations is known to be of low accuracy compared to other well known methods. However, It has been shown that the method perform well when applied to moderately stiff problems. In this present study, the nonlinear method based on the Heronian Mean (HeM), of the function value for the solution of initial value problems is developed. Stability investigation is in agreement with the known Trapezoidal method.