A Maple Implementation of the Finite Element Method for Solving Metastable State Problems for Systems of Second-Order Ordinary Differential Equations

We present a new algorithm for systems of second-order ordinary diff tial equations to calculate metastable states with complex eigenvalues of energy or to fi bound states with homogeneous boundary conditions depending on a spectral parameter. The boundary-value problems is discretized by means of the FEM using the Hermite interpolation polynomials with arbitrary multiplicity of the nodes, which preserves the continuity of derivatives of the desired solutions. For the solution of the relevant algebraic problems the Newton iteration scheme is implemented.

Authors
Chuluunbaatar G. 1, 2 , Gusev A.A. 1, 4 , Derbov V.L. 5 , Vinitsky S.I. 1, 2 , Chuluunbaatar O. 1
Conference proceedings
Computer Algebra
Publisher
Российский университет дружбы народов (РУДН)
Language
English
Pages
42-45
Status
Published
Year
2021
Organizations
  • 1 Joint Institute for Nuclear Research
  • 2 Peoples' Friendship University of Russia (RUDN University)
  • 3 Dubna State University
  • 4 N.G. Chernyshevsky Saratov National Research State University
  • 5 Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences
Keywords
fi element method; interpolation Hermite polynomials; boundary-value problem; metastable state; system of ordinary diff tial equations; Newton iteration scheme
Date of creation
16.12.2021
Date of change
16.12.2021
Short link
https://repository.rudn.ru/en/records/article/record/78615/
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