Algorithm of Numerical Solving the Parametric Sturm-Liouville Problem and Calculation of Solution Derivatives with Respect to the Parameter via the Finite-Element Method

The economical algorithm is presented for numerical solving with the given accuracy of the parametrical Sturm-Liouville problem with the third type boundary conditions on the finite interval by the finite-element method with automatical shift of the spectrum. The algorithm includes the calculation with given accuracy a set ∼ 10-50 of the eigenvalues, eigenfunctions and their first derivatives with respect to the parameter, and integrals - matrix elements between eigenfunctions and their derivatives with respect to the parameter. Efficiency of the algorithm is demonstrated by numerical analysis of the parametric integrable problem with the parametric third type boundary conditions.

параметрическая задача Штурма-Лиувилля, метод конечных элементов, метод Канторовича