Computing the eigenvalues of a class of nonlocal Sturm-Liouville problems

In this paper, we shall use the regularized sampling method introduced recently to compute the eigenvalues of Sturm-Liouville problems with nonlocal conditions {−y″+q(x)y=λy,x∈[0,1]χ0(y)=0,χ1(y)=0, where q∈L1 and, χ0 and χ1 are continuous linear functionals defined by χ0(y)=∫01[y(t)dψ1(t)+y′(t)dψ2(t)],χ1(y)=∫01[y(t)dϕ1(t)+y′(t)dϕ2(t)], where χ0 and χ1 are independent, and ψ1,ψ2, ϕ1 and ϕ2 are functions of bounded variations. Integration is in the sense of Riemann-Stieltjes. A few numerical examples will be presented to illustrate the merits of the method, and comparisons will be made with the exact eigenvalues when they are available.