[PDF] Top 20 Approximating solutions of nonlinear second order ordinary differential equations via Dhage iteration principle

... for all t ∈ J. Clearly, C ( J, R ) is a Banach space with respect to above supremum norm and also partially ordered w.r.t. the above partially order relation ≤ . It is known that the partially ordered Banach space ... See full document

... The Dhage iteration principle or method ( in short DIP or DIM) developed in Dhage [11,12,13,14] may be formulated as “ monotone convergence of the sequence of successive approximations to the ... See full document

... The Dhage iteration principle or method (in short DIP or DIM) developed in [3, 4, 5, 6, 7] is relatively new to the literature on nonlinear analysis, particularly in the theory of ... See full document

... Several numerical methods based on the use of polynomial functions (Power series, Legendre, Chebyshev, e.t.c) have been used as basis function to develop numerical methods for direct solution of (1.1) using interpolation ... See full document

... The Dhage iteration principle or method (in short DIP or DIM) developed in Dhage [3, 4, 7] may be described as “ the sequence of successive approximations of a nonlinear equation ... See full document

... of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ... See full document

... of nonlinear hybrid functional differential equations involving a delay and explain the power of a new iteration method in ...approximate solutions of an initial value problem of first ... See full document

... Definition 2.4. [Dhage 4] An operator A on a partially normed linear space X into itself is called partially bounded if A(C) is bounded for every chain C in X . A is called uniformly partially bounded if all ... See full document

... above nonlinear differential equation with maxima ...the solutions via classical methods of Schauder and Banach fixed point ...the differential equation with maxima ... See full document

... The Dhage iteration principle which states that the sequence of successive ap- proximations of a nonlinear equation beginning with a lower or an upper solution converges monotonically to its ... See full document

... (1.8) Nonlinear functional differential equations occur in sev- eral problems of dynamic systems and have been studied in the literature for a long time via functional analytic meth- ... See full document

... By Lemma ., the boundary value problem (.) has at least three nontrivial solutions containing a positive solution, a negative solution and a sign-changing solution. Remark By Theorem . and Theorem ., we ... See full document

... as nonlinear oscillations [, ], fluid me- chanical and nonlinear elastic mechanical phenomena [–] are associated with the peri- odic solutions of nonlinear high-order differential ... See full document

... Finally, when we look at ODEs (1)–(5), we see that ODEs (1)–(4) are linear and ODE (5) has a slightly modified nonlinear form. Next, ODEs (6) and (7) include and improve ODEs (1)–(4) from the linear cases to the ... See full document

... In this paper, we have presented a semi-analytical method (DTM) for solving a certain class of ODEs. The DTM has advantages over other numerical techniques as it does not involve linearization, discretization or ... See full document

... wave solutions of NLPDEs play an important role in the study of nonlinear physical ...exact solutions to nonlinear evolution equations (NLEEs) has long been a major concern for both ... See full document

... The equations are based on both human and mosquito population, infection rates of human and mosquito per unit time, rescaling of critical population of each class by total species population and bifurcation ... See full document

... R n → R n , H ∈ C 0 ( R n ) and P ∈ C ( R n ) where C 0 ( R n ) is the set of all continuous function differentiable once on R n and C ( R n ) is the set of all continuous function on R n . Let R denote the real line −∞ ... See full document

... functional differential equations have been studied in recent ...functional differential equations received much less attention, which is due mainly to the technical difficulties arising in ... See full document

... By a solution of (E) we mean a function x(t) : [T , ∞ ) → R , T ≥ a which is continuously differentiable together with p(t)ϕ(x (t)) on [T , ∞ ) and satisfies (E) at every point of [T, ∞ ). It is easily seen (see []) that ... See full document