Boundary value problems for higher order differential equations[MatSciRep: 98]

Abstract

Boundary value Problems(BVPs) for ordinary linear or nonlinear differential equations occur in many branches of applied mathematics, theoretical physics, and engineering, the most significant among them being the boundary layer theory, the study of stellar interiors and control and optimization theory. For a given differential equation of order (n > or = 2) or a system of differential equations, when the conditions are prescribed at two points we say two point problem. If the conditions are prescribed at more than two points, we say multipoint problem. For a given dynamical system with n degrees of freedom, there may be available exactly n states observed at n different times. A mathematical description of such a system results in an n point BVP. The discretization of certain BVPs for partial differential equations over irregular domains with the method of lines also forms MPBVP.