Laguerre Polynomial Solutions of a Class of Delay Partial Functional Differential Equations

Abstract

In this study, we develop a novel matrix collocation method based on the Laguerre polynomials to find the approximate solutions of some parabolic delay differential equations with integral terms subject to appropriate initial and boundary conditions. The method reduces the solution of the mentioned equations to the solution of a matrix equation which corresponds to system of algebraic equations with unknown Laguerre coefficients. Besides, the error analysis together with numerical results are performed to illustrate the efficiency of our method computationally.

Lerch matrix collocation method for 2D and 3D Volterra type integral and second order partial integro differential equations together with an alternative error analysis and convergence criterion based on residual functions

“…When the approximate solution u N (x, y, λ) and its derivatives are substituted in (1.1), and the approximate solution u N (x, y, z, λ) and its derivatives are substituted in (1.3), the resulting equations must satisfy approximately [4,10,11,18,27,39];…”

Solving Fractional Fredholm Integro-Differential Equations by Laguerre Polynomials

“…Laguerre polynomials are used to solve some integer order integro-differential equations. These equations are given as Altarelli-Parisi equation (Kobayashi et al 1995), Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation (Schoeffel 1999), Pantograph-type Volterra integrodifferential equation (Yüzbaşı 2014), linear Fredholm integro-differential equation (Baykus Savasaneril & Sezer 2016;Gürbüz et al 2014), linear integro-differential equation (Al-Zubaidy 2013), parabolic-type Volterra partial integro-differential equation (Gürbüz & Sezer 2017a), nonlinear partial integro-differential equation (Gürbüz & Sezer 2017b), delay partial functional differential equation (Gürbüz & Sezer 2017c). Besides, Laguerre polynomials are used to solve the fractional integro-differential equation (Mahdy & Shwayyea 2016).…”

A method for fractional Volterra integro-differential equations by Laguerre polynomials

“…Laguerre polynomials are used to solve some integer order integro-differential equations. These equations are given as Altarelli-Parisi equation [42], Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation [43], pantograph-type Volterra integro-differential equation [44], linear Fredholm integro-differential equation [45,46], linear integrodifferential equation [47], parabolic-type Volterra partial integro-differential equation [48], nonlinear partial integro-differential equation [49], delay partial functional differential equation [50]. Besides, Laguerre polynomials are used to solve the fractional Fredholm integro-differential equation [51].…”