استخدام المتسلسلات في حل مسائل القيم الحدية (منظومة شتروملوفيل)

Abstract

Abstract: In general, sturm-Lioville system is obtained by applying the separation of variables to boundary or elementary value problems of second order, since the sturm-Lioville system contains a homogeneous differential equation of the second order with two terms for each a<x< b.Therefore, the main objective of this paper is to solve the sutrm-Liovill system using power series when x=x_0 is a fair point of the system. By applying the boundary conditional, general solution of the stutrm-liovill system is achieved and it is found that each eigenvalue λ_ncorresponds to an eigenfunction y_n (x)and these functions are linearly independent and orthogonal solutions within the period a<x<b.