Recent developments in applied mathematics and mechanics: theory, experiment and practice. Devoted to the 80th anniversary of academician N.N.Yanenko

Akademgorodok, Novosibirsk, Russia, June 24 - 29, 2001

Abstracts

Russian participants

Defect of the accuracy of differential equations in numerical solution

Minailos A.N.

Central Aerohydrodynamic Institute (Moscow)

The differential equations (DE) – into finite-differential solutions – describe integral lows (IL) with accuracy but not higher order, then second, if the coefficients of equations contains the products of functions. Therefore, for all methods with DE (for example, mechanics of liquids and gases, or dynamics of movement of body with changeable mass, and so ) the use the schemes with the approximation order higher then second is not have the practical sense, but so increase the calculation mass.

For solutions of problems with greater then second approximation order it is need use IL of conservations with the corrections of I. V. Petuchov’s ( J. Comput. Mathem. Mathem. Phys. 1, 1961, 2). Such high approximation order is vital necessary for the solutions of rigid equations (Minailos, J. Comput. Mathem. Mathem. Phys. 38,1998,7) with very little coefficients by senior derivatives (Navier-Stokes, Reynolds turbulent movement, wave equations for EM). Defect DE demand of development any divisions of computational mathematics.

Full Text in Russian: PDF (268 kb)
Note. Abstracts are published in author's edition

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