Open Access Open Access  Restricted Access Subscription or Fee Access

Numerical algorithm for approximate solution of the third -order differential equation with boundary value problems

Ping Li, Jing Niu

Abstract


In this paper, we present an efficient numerical algorithm to solve the third-order system of boundary value problems based on the reproducing kernel Hilbert space method (RKHSM). Using reproducing property and the existence of orthogonal basis in the reproducing kernel Hilbert space, we obtain a representation of exact solution with form of series and its approximate solution by truncating the series. The advantages of our approach lie in the fact that accuracy of numerical computation is higher, on the other hand, the approximate solution and its derivatives converge uniformly to the exact solution and its derivatives. Moreover, the effectiveness of the presented method is illustrated with two numerical examples.

Keywords


Numerical algorithm; approximate solution; reproducing kernel space; linear operator.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.