TITLE:
The Exact and Approximate Solutions of Some Boundary Value Problems in Domains with Angular Points of the Boundary
AUTHORS:
Irina Menshova, Mikhail Kovalenko
KEYWORDS:
Boundary Value Problems, Exact and Approximate Solutions
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.1,
January
4,
2017
ABSTRACT:
On the basis of the exact solution of biharmonic problems of elasticity theory in a half-strip one possible reason is shown of those problems that arise when an approximate or numerical approaches leading the solution of boundary value problems to infinite systems of linear algebraic equations. Construction of exact solutions of some boundary value problems for differential equations in partial derivatives is not possible without their extensions to Riemann surfaces. Moreover, each of the boundary value problem corresponds to its Riemann surface. This fact is important to consider when developing an effective approximate and numerical methods of solving boundary value problems.