Solving Initial Value Problems with Mendeleev’s Quadrature

This article presents the Mendeleev method to solve the ini- tial value problems. The construction of this method using Mendeleev’s quadrature is due to Pleshakov [Comp. Math. and Math. Phys., 52 2012), 211-212.] to approximate the integral f(s, Y (s))ds. We derive the local truncation error and show the stability region of the pro-posed method. The computational comparisons show that Mendeleev’s method is better than Euler’s method, midpoin method and Heun’s method