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Inc, Mustafa; Akgül, Ali; Kılıçman, Adem

Numerical solutions of the second-order one-dimensional telegraph equation based on reproducing kernel Hilbert space method. (English) Zbl 1470.65181

Abstr. Appl. Anal. 2013, Article ID 768963, 13 p. (2013).
Summary: 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 from this 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.

Cited in 11 Documents

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35J25 Boundary value problems for second-order elliptic equations
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\textit{M. Inc} et al., Abstr. Appl. Anal. 2013, Article ID 768963, 13 p. (2013; Zbl 1470.65181)
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References:

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