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Article information
2001 , Volume 6, ¹ 3, p.103-112
Filimonov M.Y.
On represantation by new constructions of consistent special series of solutions of non-linear partial differential equations
New constructions of consistent special series for representation of solutions of non-linear partial differential equations are presented. This approach is the continuation of the special series method. The main feature of this method is constructive representation of solutions of non-linear equations as the series on the powers of special basic functions with recurrently calculated coefficients found from solutions of ordinary differential equations. It is shown that these series can be used for solving boundary-initial problems with exact satisfaction of boundary conditions. The convergence area of suggested series is investigated and the results of numerical experiments are presented.
[full text] Classificator Msc2000:- *35C10 Series solutions, expansion theorems
- 35K55 Nonlinear PDE of parabolic type
- 35L70 Nonlinear second-order PDE of hyperbolic type
- 65M12 Stability and convergence of numerical methods
- 65M70 Spectral, collocation and related methods
Keywords: initial-boundary value problem, special series method, convergence, special basic function, nonlinear partial differential equations
Author(s):
Filimonov Mikhail Yurjevich
Dr. , Senior Scientist
Position: Leading research officer
Office: Institute of Mathematics and Mechanics UrB RAS
Address: 620219, Russia, Ekaterinburg, S.Kovalevskaya str., 16
Phone Office: (343)3753509
E-mail: fmy@imm.uran.ru
Bibliography link:
Filimonov M.Y. On represantation by new constructions of consistent special series of solutions of non-linear partial differential equations // Computational technologies. 2001. V. 6. ¹ 3. P. 103-112
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