Galerkin's method for constructing solutions to the problems of celestial mechanics.

Details Galerkin's method for constructing solutions to the problems of celestial mechanics. Galerkin's method for constructing solutions to the problems of celestial mechanics.

Oct 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997kosis..35..487k&link_type=abstract

Kosmicheskie Issledovaniia, Tom 35, No. 5, p. 487 - 494

Physics

Celestial Mechanics: Numerical Methods

Scientific paper

Conventionally, the Cauchy problem for a system of differential equations is interpreted as a nonlinear functional equation. The solution belongs to a Sobolev space of the vector-valued functions, which is utilized for constructing finite-dimensional Galerkin approximations. Convergence in Sobolev's metric produces uniform convergence. One can use periodic functions as basic ones, to obtain oscillating solutions. Problems of celestial mechanics are such that, in most cases one can construct a finite-dimensional (i.e. represented in the form of the finite combinations of the basis functions) approximation to the exact solution.

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