Geometric Analysis of a Nonlinear Boundary Value Problem from Physical Oceanography

The Numerical Solution of Three Point Third Order Boundary Value Problems in Odes

“…The numerical approximation of and at nodal point will be respectively denoted by and . Applying these notations at node , the problem reduced to the following discrete problem, (3) and boundary conditions are and…”

“…The study and explaining problems in social and natural sciences one of the best methods is mathematical modeling and application of different orders of differential equations. Third order differential reported on the mathematical theory of channel flow in fluid dynamics by Jayaraman [1], the thyroid-pituitary homeostatic mechanism in biology by Danziger [2], physical oceanography by Dunbar [3], an active pulse transmission line simulating nerve axon by Nagumo [4], sandwich beam by Krajcinovic [5], Nagumo equation by McKean [6] and the references therein. To solve these problems analytically in realistic conditions is some time either not possible or very difficult.…”

Optimal interval lengths for nonlocal boundary value problems associated with third order Lipschitz equations

“…Such equations arise in models for boundary layer theory in fluid mechanics; as for example, when considering convection in a porous medium or a flow adjacent to a standing wall; cf. [1,6,9,12,20,35,36,38,39]. Works for third order equations have also dealt with upper and lower solutions, multiple solutions, nonlinear eigenvalue problems, periodic solutions, monotone boundary conditions, limit point and limit circle criteria, cf.…”

“…And as a consequence, solutions of the boundary value problem (1):(7) will be unique on such subintervals. U for all t ∈ (a, b), for which the boundary value problem (9):(10) has a nontrivial solution for some a < t 1 < t 2 < b, and if x 0 (t) is a time optimal solution satisfying (12) where d − c is a minimum, then x 0 (t) is a solution of (17) on [c, d].…”

Quartic non-polynomial spline approach to the solution of a system of third-order boundary-value problems

“…The wide class of odd-order obstacle boundary-value problem of unrelated obstacle, moving, free, contact and equilibrium problems arising in transportation, economics, and optimization can be studied via the general variational inequality approach and has important applications in other branches of pure and applied sciences (see for example Baiocchi and Capelo [6], Boersma and Molenaar [7], Cottle, Giannessi and Lions [8], Cranck [9], Dunbar [10], Giannessi [12] and Lewy and Stampacchia [13]). One of the most interesting and difficult problems in this theory is the development of an efficient and implementable method for solving variational inequalities.…”