Green's Function For Linear Differential Operators In One Variable

2013/01/06 by Adel Kassaian, Kassaian, Adel
Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1301.1004

openalex publication_date 2013/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

General formula for causal Green's function of linear differential operator of given degree in one variable is given according to coefficient functions of differential operator as a series of integrals. The solution also provides analytic formula for fundamental solutions of corresponding homogenous linear differential equation as series of integrals. Furthermore, multiplicative property of causal Green's functions is shown and by which explicit formulas for causal Green's functions of some classes of decomposable linear differential operators are given. A method to find Green's function of general linear differential operator of given degree in one variable with arbitrary boundary condition according to coefficient functions of differential operator is demonstrated.

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