Advances in Differential Equations and Control Processes
Volume 8, Issue 2, Pages 67 - 81
(November 2011)
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REPRODUCING KERNEL METHOD FOR INTEGRO-DIFFERENTIAL EQUATION WITH ABEL KERNEL
Li-Hong Yang, Ji-Hong Shen and Yue Wang
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Abstract: In this paper, we use the reproducing kernel method (RKM) to solve linear integro-differential equations with Abel kernel. Employing the reproducing kernel function, we construct a complete system in space The exact solution of the equation is represented by the complete system in the reproducing kernel space By comparing with the method used in [8], RKM has the following advantages, including the speed of the convergence is fast, and the precision is high, and the singularity is overcame better. And the RKM is efficient for the every real positive number l. |
Keywords and phrases: singular kernel, approximate solution, reproducing kernel space. |
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