Galerkin-Bubnov

In the mathematical literature, the Galerkin method is also known as Galerkin-Bubnov, while the case Wj / Petrov-Galerkin [30,68] and is used in special finite element formulations, such as those where the heat transfer is governed by convective effects. The application of Galerkin s method in the finite element method will be covered in detail in Chapter 9 of this textbook. 

In the standard Galerkin method (also called the Bubnov-Galerkin method) weight functions in the weighted residual statements are selected to be identical... 

Variational difference methods (the Ritz method and the Bubnov-Ga-lerkin method). The Ritz and the Bubnov-Galerkin variational methods have had considerable impact on complex numerical modeling problems and designs of difference schemes. 

So, the three-point scheme (30) (32) constructed by the Ritz method is identical with scheme (12) obtained by means of the IIM. In contrast to the Ritz method the Bubnov-Galerkin method applies equally well to... 

When the coordinate functions y>iix) = y x — x )/h) are chosen by an approved rule as suggested before, the Ritz and the Bubnov-Galerkin methods coincide with the finite element method. 

INVESTIGATION OF PERIODIC SOLUTIONS OF SYSTEMS WITH AFTEREFFECT BY BUBNOV-GALERKIN S METHOD... 

The trigonometric polynomial x (r) satisfying (1.4) is called Bubnov-Galerkin s approximation of the mth order. The system (1.4) can be rewritten as follows... 

Section 4 Existence and Convergence of Bubnov-Galerkin s Approximations 93... 

Assume that the variational system which corresponds to the exact periodic solution x(t) of the system (1.1) possesses Green s function satisfying the condition (2.3). Then, for all sufficiently large m, Bubnov-Galerkin s approximations exist and converge uniformly as ffi oo to the exact periodic solution x(t). 

Let us clarify under what conditions the existence of Bubnov-Galerkin s approximations jc (t) of an arbitrary order m mo involves the existence of periodic solutions to the system of differential equations (1.1). 

Proof. According to the definition of Bubnov-Galerkin s approximations, the function x lf) satisfies the equation... 

Taking condition (c) and (5.4) into account, we can write the mth Bubnov-Galerkin s approximation in the form... 

Application of Bubnov-Galerkin s Method to the Investigation of Periodic Solutions for Some Classes of Systems of Integro-Differential... 

Then one can always find si ciently large m such that Bubnov-Galerkin s approximations x = xjlf) exist for al m > ntQ and converge to the exact periodic solution X = x t) as m- oo. Moreover, these approximations sati the inequality... 

Construction of Quasiperiodic Solutions of Systems uith Lag by Bubnov-Galerkin s Method... 

Let us show that a periodic solution of (3.4) can be constructed with the help of Bubnov-Galerkin s method. 

Bubnov-Galerkin s method for construction of periodic solutions of integ-... 

Bubnov-Galerkin s method for nonlinear periodic systems of integro-differential equations with infinite cfiereffect. Preprint Akad. Nauk Ukrain. SSR, Inst. Matemadki 82.50, Kiev, 1982. 

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