This survey is intended to give an overview of the existing numerical methods and techniques for solving a multi-parameter eigenvalue problem. It also collects some well-known examples of multi-parameter spectral problem and its practical applications in different scientific areas.
Methods of local gravitational field presentation using nonorthogonal functions are considered. Analysis of SCHA, ASHA and TOSCHA techniques of local field modeling on spherical cap and spherical segment is accomplished according to density distribution of initial data. Approximate formula for finding eigenvalues of differential equation of associated spherical functions is found and compared with other formulas. This approach involves using of associated Legendre functions of integer degree and noninteger order. These functions form two sets of functions.