Numerical solution of eigenvalue problems for Hamiltonian systems
The paper concerns an eigenvalue problem for a Hamiltonian system of ordinary differential equations with nonlinear dependence on a real eigenparameter \(\lambda\). Separated boundary conditions are treated. The coefficients are at least continuously differentiable as a function of \(\lambda\). Using \(\Theta\) matrices of Atkinson the author constructs an increasing integer-valued function \(M(\lambda)\) whose only points of increase are discontinuities at the eigenvalues, and the size of the discontinuity is equal to the multiplicity of the corresponding eigenvalue. The author describes two alternative approaches to the problem of computing the function \(M(\lambda)\). Some numerical experiments using these algorithms are presented. The author informs that both codes are fully documented and are written in Fortran 77, and will be available in netlib/aicm/sl11f and netlib/aicm/sl12f.
scientific article; zbMATH DE number 784490