Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type | Zendy

Iryna Komashynska | Zendy; Mohammed AlSmadi | Zendy

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Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type

Author(s) -

Iryna Komashynska,

Mohammed AlSmadi

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/459509

Subject(s) - mathematics , kernel (algebra) , monotone polygon , nonlinear system , iterative method , fredholm integral equation , integral equation , series (stratigraphy) , simple (philosophy) , fredholm theory , boundary value problem , convergent series , type (biology) , class (philosophy) , mathematical analysis , mathematical optimization , computer science , pure mathematics , paleontology , philosophy , physics , geometry , ecology , epistemology , quantum mechanics , artificial intelligence , biology , power series

We present an efficient iterative method for solving a class of nonlinear second-order Fredholm integrodifferential equations associated with different boundary conditions. A simple algorithm is given to obtain the approximate solutions for this type of equations based on the reproducing kernel space method. The solution obtained by the method takes form of a convergent series with easily computable components. Furthermore, the error of the approximate solution is monotone decreasing with the increasing of nodal points. The reliability and efficiency of the proposed algorithm are demonstrated by some numerical experiments

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