Integral transform based decomposition methods and runge kutta type methods for delay differential equations

Abstract

In this thesis, integral transform-based decomposition methods and Runge-Kutta type newlinemethods are presented for solving delay differential equations (DDEs). To start with, Integral newlinetransform-based decomposition methods which is the combination of a particular integral newlinetransform and the Adomian decomposition method (ADM) are presented to solve linear and newlinenon-linear DDEs. In this thesis, four recent integral transforms have been considered and newlinecombined with ADM to solve linear and non-linear DDEs. newlineNext, the higher order derivative Runge-Kutta methods of 2-stage third order and 3- newlinestage fourth order have been proposed to solve linear and non-linear DDEs. Then the newlinemultiderivative explicit Runge-Kutta method of 2-stage fourth order has been constructed to newlinesolve DDEs. Consequently, the inverse Runge-Kutta methods of order 3 and 4 have been newlineproposed to solve DDEs. newlineThe stability polynomials of these Runge Kutta-type methods are derived, and their newlinecorresponding stability regions are obtained. The convergence analysis of these methods is newlinealso discussed. The delay term is approximated by using Lagrange interpolation in these three newlinetypes of Runge Kutta methods. newlineNumerical examples of delay differential equations with constant, time dependent, newlinestate dependent and pantograph type delays have been considered to demonstrate the newlineefficiency of all the proposed methods. Finally, the dynamic behavior of infectious disease newlinemodel has been analyzed through the inverse Runge-Kutta method and compared with the newlinenumerical simulations already given in the literature. newline