Comparative analysis of some direct methods for solving problems in mathematical physics

Author(s):  V.I. Vanko, Prof., Bauman Moscow State Technical University, Moscow, Russia,

N.K. Kosakyan, Bauman Moscow State Technical University, Moscow, Russia,

Issue:  Volume 50, № 2

Rubric:  Physics. Mathematical modeling

Annotation:  The paper discusses the problem of the deflections of a rectangular membrane (rigid fixed contour with sides 0≤x≤ a,0≤ y≤b) ) constant tension’s, loaded uniformly distributed pressure. The problem is solved by direct methods: Ritz (Bubnov-Galerkin), least squares and Kantorovich. These solutions are compared according to the residual norm. By the method of variables separation, the exact solution of the problem (in series) is constructed, with which the solutions mentioned above are compared. It is found out that the solution by the Kantorovich method “pointwise” has the smallest deviation from the exact solution.

Keywords:  membrane under pressure, Dirichlet problem, methods: Ritz, least squares, Kanto-rovich, variables separation; a comparative analysis of the solutions obtained

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