In this work, an orthogonal polynomial with weight function w (x)= x2+ x+ 1 in the interval [-1,
1] was constructed and used as the basis function to develop block methods, using …

In this work, a convergent hybrid block method (CHBM) with two off-grid points for direct
integration of first, second, and third-order initial value problems (IVPs) is proposed. The …

A novel and efficient algorithm for the concurrent numerical solution of second, third and
fourth orders of ordinary differential equations is studied in this article. Collocation and …

This paper presents an integrator based on a linear polynomial and a logarithmic function
for the numerical solutions of initial value problems (IVPs) of first order Ordinary Differential …

A numerical integrator of order five is developed for the solutions of systems of first order
initial value problems. An assumed solution is used to represent the actual solution, which is …

Derivation of a two-step hybrid block method that provides a numerical solution for a general
second-order initial value problems of ordinary differential equations directly is presented in …