Abstract
Among boundary value problems(BVP) for partial differential equations (PDE),of considerable promise for investigation is a class of problems that can be reduced to difference, functional, differential functional and other relevant equations. This class consists mainly of problems marked by the familiar representation of general solution for the corresponding PDE(in particular, this can be found by the method of characteristics).In this paper we consider the initial-boundary value problem of the linear wave equation wtt(x,t)-wxx(x,t)=0 on an interval with the boundary condition at the left endpoint is wx(0,t)=rw(0,t), while the boundary condition at the right endpoint has cubic nonlinearity of a vander Pol type, wx(1,t)=αwt(1,t)-β(wt(1,t))3, α,β〉0 .2. Formulation --------------------------------------13. Preliminaries--------------------------------------54. Numerical Simulation -----------------------------134.1 Steady state --------------------------------------134.2 Compute x0 ----------------------------------------144.3 Bifurcation diagram -------------------------------144.4 Lyapunov exponents --------------------------------144.5 Numerical Simulation of PDE ------------------145. Conclusion ---------------------------------226.References -----------------------------------------------23