KANTBP 4M - program for solving boundary problems of the self-adjoint system of ordinary second order differential equations

Authors: A.A.Gusev, L. Le Hai, O.Chuluunbaatar, S.I.Vinitsky
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Environment: MAPLE (tested in versions 14, 16, 17 and 18) / Windows

The program of KANTBP 4M implemented in the computer algebra system MAPLE for solutions to a given accuracy of boundary problem and eigenvalue problem for the self-adjoint system of ordinary differential equations of the second order with continuous or piecewise continuous real or complex-valued coefficients. The desired solution in a finite interval of the real-valued in the independent variable subject to homogeneous boundary conditions: Dirichlet and/or Neumann, and/or third kind. Discretization of the boundary problems are implemented by the finite element method with the interpolation Hermite polynomials preserves the property of continuity of derivatives of the desired solutions [1]. Solutions of algebraic problems are performed using the built-in procedures of the linear algebra.

For the reduction of the boundary-valued problem or the scattering problem with a different number of open channels in the two asymptotic regions to the boundary problems on a finite interval, the asymptotic boundary conditions for large absolute values of the independent variable are approximated homogeneous boundary conditions of the third kind. The program calculates the energy eigenvalues or the scattering matrix composed of square matrices amplitude reflection and rectangular matrices of transmission amplitudes, and wave functions in the close-coupled channels and Kantorovich [2] methods at specified basis functions.

For the calculation of metastable states with complex eigenvalues of energy, or to solve the problem for bound states with boundary conditions depending on the spectral parameter the Newtonian iteration scheme is implemented [3].

Test Examples 01-16 of solving boundary problems and eigenvalue problems of quantum mechanics are given in the detailed description.

Sources and the detailed description (pdf) are submitted


  1. A.A. Gusev et al, Lecture Notes in Computer Science 8660, 138-154 (2014).
  2. Z. A. Vlasova Trudy Mat. Inst. Steklov., 53 (1959), 16-36 .
  3. A.A. Gusev et al, Lecture Notes in Computer Science 9301, 182-197 (2015).

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