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

Ping Li, Jing Niu


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.


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

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