An effective metaheuristic algorithm to solve the higher-order boundary value problems, called a genetic programming technique is presented. In this paper, algorithm, which depends on syntax tree representation, employed obtain analytical solutions of higher- order differential equations with conditions. The proposed can be produce an exact or approximate solution when classical methods lead un...

In this paper, we consider a discontinuous, fully nonlinear, higher-order equation on the half-line, together with functional boundary conditions, given by general continuous functions dependence several derivatives and asymptotic information (n−1)th derivative of unknown function. These conditions generalize usual data allow other types global assumptions function its derivatives, such as nonl...

Let f : [a, b] × R n+1 → R be a Carathéodory's function. Let {t h }, with t h ∈ [a, b], and {x h } be two real sequences. In this paper, the family of boundary value problems´x is considered. It is proved that these boundary value problems admit at least a solution for each k ≥ ν, where ν ≥ n + 1 is a suitable integer. Some particular cases, obtained by specializing the sequence {t h }, are poi...

Abstract—Bringing forth a survey on recent higher order spline techniques for solving boundary value problems in ordinary differential equations. Here we have discussed the summary of the articles since 2000 till date based on higher order splines like Septic, Octic, Nonic, Tenth, Eleventh, Twelfth and Thirteenth Degree splines. Comparisons of methods with own critical comments as remarks have ...