Numerical solution of vector Sturm-Liouville problems with Dirichlet conditions and nonlinear dependence on the spectral parameter (Q1687805)

This paper concerns the numerically computation of the eigenvalues of self-adjoint regular vector Sturm-Liouville problems with Dirichlet boundary conditions and the matrix coefficients are supposed to be nonlinear functions of the spectral parameter \(\lambda\). Specifically, the authors consider the following Sturm-Liouville problem \[ \left(P(x,\lambda)Y'\right)'+R(x,\lambda)Y=0, 0<x<l, Y(0)=Y(l)=0, \] where \(Y\) is an \(s\)-vector function, \(P\) and \(R\) are \(s\times s\) matrix functions defined on the interval \([0,1]\), and \(\lambda\) is a positive real number. Further assumptions concerning the behavior of the coefficients \(P\), \(P^{-1}\) and \(R\) are assumed to hold on some extended interval of the variable \(x\). The authors apply the so-called ``numerical-analytical iterative method'' based on spectral correction for solving the problem. Test examples are presented.