Sturm - Liouville Problem
Sturm - Liouville Problem: The Sturm - Liouville Problem is a special class of linear homogeneous boundary value problem given in the following definition. Definition : Consider a second order homogeneous linear differential equation of the form d/dx [p(x) dy/dx ] + [q(x) + λ γ(x)]y=0, a≤x≤b ...............(1) where p, q and γ are real - valued continuous functions on [a,b] and λ is real parameter . Further consider the following two sets of prescribed conditions a1 y(a) + a2 y'(a) = 0} }...................(2) b1 y(b) + b2 y'(b) = 0} y(a) = y(b) , y'(a) = y'(b) , p(a) = p(b) .........(3) where the real constants a1 and a2 are not both zero and b1 and b2 are not both zero . A boundary value problem consisting of equation(1) with either the boundary condition (2) or the boundary condition (