Interpolation problems arise in many areas where there is a need to construct a continuous
surface from irregularly spaced data points. This problem has a number of solutions and …

This article develops an efficient direct solver for solving numerically the high-order linear
Fredholm integro-differential equations (FIDEs) with piecewise intervals under initial …

A new operational matrix for integration of Bernoulli polynomials is introduced. By using this
new operational matrix of integration and the so-called collocation method, linear Volterra …

In this paper, a new matrix approach for solving second order linear partial differential
equations (PDEs) under given initial conditions has been proposed. The basic idea includes …

Toward Deep Neural Networks: WASD Neuronet Models, Algorithms, and Applications
introduces the outlook and extension toward deep neural networks, with a focus on the …

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 …

Bernoulli polynomials have many useful properties, but the main disadvantage of these
polynomials is that they are not orthogonal. In this paper, we offer an explicit representation …

This paper contributes a new matrix method for the solution of high‐order linear complex
differential equations with variable coefficients in rectangular domains under the considered …

A matrix approach to Sheffer polynomial sequences is proposed; in particular, two different
determinantal forms of Sheffer sequences are given, the one as the function of a polynomial …

The purpose of this paper is to introduce a novel approach based on the operational matrix
of orthonormal Bernoulli polynomial for the numerical solution of the class of singular …