[PDF] Top 20 Two dimensional product type system of difference equations solvable in closed form

... classes of the class in () has been previously treated in our papers on product-type sys- tems, so that all the formulas presented here should be new. The formulas are obtained by further developing the ... See full document

... finite difference method for solving 2-dimensional diffusion equation is ...nite difference formulation and its convergence and sta- ...a system of linear equations should be ... See full document

... the system. Some equations in [] are product-type ones, but they have additional multipliers, which suggested us to study the solvability of the generalizations of system () ... See full document

... the form of known hyperbolic-cotangent sum ...difference equations are candidates for solvable ones, the fact known for a long time (the observation can be found in the old book [7], and it would not ... See full document

... introduced two coefficients and also got solvable systems (this was done for the first time in [], and somewhat later in ...few solvable product-type systems of difference ... See full document

... on product-type systems [] investigated the case k = m = , l = s = , and our original intention was to study, as usual, the long-term behavior of their ...related system with three dependent ... See full document

... where the function f satisfies the following condition: f (t, t, . . . , t) ∼ t, as t → 0. When f (t) = 1+bt t , we have f (t) ∼ t, as t → 0, and a simple solvable difference equation is obtained (see, e.g, [6, ... See full document

... the form of the solutions of this type of systems could be given by studying all the quan- tities appearing there in ...on product-type systems see [], [] and ... See full document

... difference equations and systems not stemming from differential ones (see, ...difference equations and systems has re-attracted recent attention (see, ...complicated equations and systems into simpler ... See full document

... The following result gives information on local dynamics near a fixed point of a map when there exists a characteristic vector whose coordinates have negative product and such that the associated eigenvalue is ... See full document

... , (6) where the parameters c an p are positive real numbers. And who proved that all positive solutions of system (6) are bounded when and so forth (see [16]). In addition, related research can also be seen in ... See full document

... the problem of periodicity of their solutions (see, for example, [, , , , , , , ], and the references therein), while global attractivity results can be found, for example, in [, , , ]. For the ... See full document

... of solvable type, ...is solvable. Some cases where ρ of solvable type is known to be modular are: when n = 2 ([La2], [Tu]); when n = 3 and ρ is induced ([JPSS]); when n = 3 and ρ is the ... See full document

... the system at the high values of the Reynolds number, and analyses the evolution of the dynamic be- havior of the ...our system behaves in a way similar to that predicted by Ruelle and ...chaotic ... See full document

... provides closed form solution but it is usually limited with regard to the complexity ...one- dimensional analytical solutions were ...one- dimensional advection-dispersion equation was ... See full document

... P u u u u u  = (2.1) where P is a multivariate polynomial in its arguments. In the following, it is explained the basic for implement- ing Exp-function method. Taking the change of variable ξ = kx + wy , gives u x ( ) = ... See full document

... 3. Nonlinear wave equation in two variables. It is easy to show that θ(x,y) is a solution of the wave equation in two variables if and only if θ(x,iy) is a solution of the Laplace equation in two ... See full document

... Fuzzy difference equations have been studied to some extent, for example see ...volterra difference equations and prove some basic facts about this ...this equations in terms of ordi- ... See full document

... The geometry of the problem and the coordinate system are shown in Fig. 1, in which x-axis and y-axis are along and normal to the vertical plate respectively. Steady and incompressible couple stress fluid along a ... See full document

... the form of multiplication of sin and cos ...resultant system of algebraic equations are solved for non zero a and ν with at least one of A Q or B Q is non ... See full document