Hybrid approximation for solutions of high-order integro-differential equations including variable delay
Abstract In this study, a numerical technique with hybrid approximation is developed for solving high-order linear integro-differential equations including variable delay under the initial conditions. These type of problems are of applications in mathematical physics, mechanics, natural sciences, electronics and computer science. The aim of this work is to investigate an approximation with the matrix forms of Taylor and Laguerre polynomials along with standard collocation points. By the reduction of the solution of this problem with regard to the matrix relations, the solution of a system of algebraic equations has been obtained. The usefulness of this algorithm has been demonstrated by num…
A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering
<p style='text-indent:20px;'>Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine learning, mechanics, economics, electrodynamics and so on. Besides, special classes of functional differential equations have been investigated in many researches. In this study, a numerical investigation of retarded type of these models together with initial conditions are introduced. The technique is based on a polynomial approach along with collocation points which maintains an approximated solutions to the problem. Beside…
A Computational Technique for Solving Singularly Perturbed Delay Partial Differential Equations
Abstract In this work, a matrix method based on Laguerre series to solve singularly perturbed second order delay parabolic convection-diffusion and reaction-diffusion type problems involving boundary and initial conditions is introduced. The approximate solution of the problem is obtained by truncated Laguerre series. Moreover convergence analysis is introduced and stability is explained. Besides, a test case is given and the error analysis is considered by the different norms in order to show the applicability of the method.
An Introduction to the Special Issue on Numerical Techniques Meet with OR - Part II
Abstract The special issue: “Numerical Techniques Meet with OR” of the Foundations of Computing and Decision Sciences consists of two parts which are of the main theme of numerical techniques and their applications in multi-disciplinary areas. The first part of this special issue was already collected in the FCDS Vol. 46, issue 1. In this second part of our special issue editorial, a description of the special issue presents numerical methods which can be used as alternative techniques for Scientific Computing and led Operational Research applications in many fields for further investigation.
Laguerre Matrix-Collocation Method to Solve Systems of Pantograph Type Delay Differential Equations
In this study, an improved matrix method based on collocation points is developed to obtain the approximate solutions of systems of high-order pantograph type delay differential equations with variable coefficients. These kinds of systems described by the existence of linear functional argument play a critical role in defining many different phenomena and particularly, arise in industrial applications and in studies based on biology, economy, electrodynamics, physics and chemistry. The technique we have used reduces the mentioned delay system solution with the initial conditions to the solution of a matrix equation with the unknown Laguerre coefficients. Thereby, the approximate solution is…
Editorial – Preface to the Special Issue on Numerical Techniques Meet with OR
Abstract This special issue of the Foundations of Computing and Decision Sciences, titled ”Numerical Techniques Meet with OR”, is devoted to the numerical techniques and their applications in real-world phenomena. The special issue and its editorial present numerical algorithms as they meet with different research topics such as, e.g., from operational research, supply chain management, geometrical structures and Covid-19 effects on financial applications. Besides, the special issue covers instructional information about numerical techniques which are useful for OR research problems and real-world applications on such issues.