Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method | Zendy

Mustafa İnç | Zendy; Ali Akgül | Zendy; Adem Kılıçman | Zendy

Open Access

Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method

Author(s) -

Mustafa İnç,

Ali Akgül,

Adem Kılıçman

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/768963

Subject(s) - mathematics , reproducing kernel hilbert space , representer theorem , kernel (algebra) , hilbert space , kernel method , simple (philosophy) , partial differential equation , mathematical analysis , numerical analysis , exact solutions in general relativity , differential equation , boundary value problem , kernel embedding of distributions , pure mathematics , computer science , artificial intelligence , philosophy , epistemology , support vector machine

We investigate the effectiveness of reproducing kernel method (RKM) in solving partial differential equations. We propose a reproducing kernel method for solving the telegraph equation with initial and boundary conditions based on reproducing kernel theory. Its exact solution is represented in the form of a series in reproducing kernel Hilbert space. Some numerical examples are given in order to demonstrate the accuracy of this method. The results obtained fromthis method are compared with the exact solutions and other methods. Results of numerical examples show that this method is simple, effective, and easy to use

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