zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Analytical solution of wave system in n with coupling controllers. (English) Zbl 1231.65248
Summary: The purpose of this paper is to consider analytical solution of wave system in R n with coupling controllers by using the homotopy perturbation method (HPM). HPM is applied to the system of linear partial differential equations, i.e. the system of waves in the two-dimensional version of system equations (1) and (2). This problem is motivated by an analogous problem in ordinary differential equations for coupled oscillators and has potential application in isolating a vibrating object from the outside disturbances. For example, rubber or rubber-like materials can be used to either absorb or shield a structure from vibration. As an approximation, these materials can be modeled as distributed springs. In this paper, HPM was used to obtain analytical solution of wave system in with coupling controllers. The method provides the solutions in the form of a series with easily computable terms. Unlike other common methods for solving any physical problem, linear or nonlinear, that requires linearization, discretization, perturbation, or unjustified assumptions that may slightly change the physics of the problem, the HPM finds approximate analytical solutions by using the initial conditions only. The method proposed in this paper is very reliable and efficient and is being used quite extensively for diversified nonlinear problems of a physical nature. The algorithm is being used for the first time on such problems.
65N99Numerical methods for BVP of PDE
35L53Second-order hyperbolic systems, initial-boundary value problems
35C10Series solutions of PDE
35C15Integral representations of solutions of PDE