In this paper, small modification on Improved Euler's method (Heun's method) is proposed to
improve the efficiency so as to solve ordinary differential equations with initial condition by …

Many of problems in engineering and science is modeled by differential equations
mathematically, therefore their solutions have an important role. Many methods have been …

This paper is devoted to study the methods corresponding families of one-step methods like
the methods of Runge-Kutta, Rosenbrock, and ObreschKov. Which have A-stable of order 2 …

We give the greatest values r1, r2 and the least values s1, s2 in (1/2, 1) such that the double
inequalities C (r1a+(1− r1) b, r1b+(1− r1) a)< αA (a, b)+(1− α) T (a, b)< C (s1a+(1− s1) b …

This paper will present the two-point block one-step method for solving stiff ordinary
differential equations (ODE s). The propose block method is A-stable and the order is three …

We present a new third order Runge Kutta method based on linear combination of arithmetic
mean, geometric mean and harmonic mean to solve a first order initial value problem. We …

A new third order weighted Runge-Kutta formula based on Centroidal Mean (CeM) is
derived and implemented. To illustrate the effectiveness of the method, a stiff problem has …

In this paper we introduce a modification of the third order Runge-Kutta method based on a
convex combination of Lehmer means. The error of this method is also presented. The …

Many problems in engineering, physical and social sciences are reduced to quantifiable
form through the process of mathematical modeling that involved differential equations …

This paper discusses a weighted fourth order Runge-Kutta method based on contra-
harmonic mean to solve ordinary differential equations. The local truncation error and …