## POTHEA

swMATH ID: | 19948 |

Software Authors: | Gusev, A.A.; Chuluunbaatar, O.; Vinitsky, S.I.; Abrashkevich, A.G. |

Description: | POTHEA: a program for computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined 2D elliptic partial differential equation. A FORTRAN 77 program is presented for calculating with the given accuracy eigenvalues, surface eigenfunctions and their first derivatives with respect to a parameter of the parametric self-adjoined 2D elliptic partial differential equation with the Dirichlet and/or Neumann type boundary conditions on a finite two-dimensional region. The program calculates also potential matrix elements that are integrals of the products of the surface eigenfunctions and/or the first derivatives of the surface eigenfunctions with respect to a parameter. Eigenvalues and matrix elements computed by the POTHEA program can be used for solving the bound state and multi-channel scattering problems for a system of coupled second order ordinary differential equations with the help of the KANTBP program [the second author et al., ibid. 177, No. 8, 649–675 (2007; Zbl 1196.81283)]. Benchmark calculations of eigenvalues and eigenfunctions of the ground and first excited states of a Helium atom in the framework of a coupled-channel hyperspherical adiabatic approach are presented. As a test desk, the program is applied to the calculation of the eigensolutions of a 2D boundary value problem, their first derivatives with respect to a parameter and potential matrix elements used in the benchmark calculations. |

Homepage: | http://cpc.cs.qub.ac.uk/summaries/AESX_v1_0.html |

Keywords: | eigenvalue and multichannel scattering problems; Kantorovich method; finite element method; multichannel adiabatic approximation; ordinary differential equations; high-order accuracy approximations |

Related Software: | KANTBP; Maple; KANTBP 2.0; POTHMF; ODPEVP; ASYMPT |

Referenced in: | 2 Publications |

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### Referenced by 8 Authors

2 | Chuluunbaatar, Ochbadrakh |

2 | Gusev, Alexander A. |

2 | Vinitsky, Sergue I. |

1 | Abrashkevich, A. G. |

1 | Chuluunbaatar, G. |

1 | Derbov, Vladimir L. |

1 | Gerdt, Vladimir Petrovich |

1 | Góźdź, Andrzej |

### Referenced in 1 Serial

1 | Computer Physics Communications |

### Referenced in 2 Fields

2 | Numerical analysis (65-XX) |

1 | Partial differential equations (35-XX) |