The present paper illustrates some classes of multivalue methods for the numerical solution
of ordinary and fractional differential equations. In particular, it focuses on two-step and …

This book presents a novel approach to umbral calculus, which uses only elementary linear
algebra (matrix calculus) based on the observation that there is an isomorphism between …

In this paper a novel operational matrix of derivatives of certain basis of Legendre
polynomials is established. We show that this matrix is expressed in terms of the harmonic …

This paper is concerned with developing two new algorithms for direct solutions of linear
and nonlinear sixth-order two point boundary value problems. These algorithms are based …

For the numerical solution of high even order differential equations with two-points Hermite
boundary conditions a general collocation method is derived and studied. Computation of …

In this paper, a new method for solving fourth-order BVPs is presented. The method is based
on the first type Lidstone interpolating function. One of the greatest features of the Lidstone …

A general procedure to determine collocation methods for high order boundary value
problems is presented. These methods provide globally continuous differentiable solution in …

A method is presented for the numerical solution of odd-order nonlinear boundary value
problems with complementary Lidstone boundary conditions. The approximate solution is …

In this paper an efficient numerical method for solving a class of multipoint boundary value
problems with special boundary conditions of Birkhoff-type is presented. After a quick …

Two new general classes of polynomial sequences called respectively odd and even
Lidstone-type polynomials are considered. These classes include classic Lidstone …