General Lagrange-hybrid functions and numerical solution of differential equations containing piecewise constant delays with bibliometric analysis

Abstract

Delay differential equations have been the topic of significant interest in scientific and engineering problems. In this manuscript, we deal with the numerical solution of delay differential equations containing piecewise constant delays. The present method is based on general Lagrange-hybrid functions (GLHFs) and collocation method. First, we define GLHFs without considering the nodes of Lagrange polynomials. The integration operational matrix and delay operational matrix of GLHFs are obtained, generally. Using the integration and delay operational matrices and collocation method, the proposed problem transforms into a system of algebraic equations. An estimation of the error is derived in the sense of the Sobolev norm. Several numerical examples are given to demonstrate the accuracy and validity of the proposed computational procedure, as the mathematical model of tumor growth in mice and HIV infection of CD4+ T-cells. Moreover, delay differential equations are studied through a bibliometric viewpoint.