## Approximate solution of BVPs for 4th-order IDEs by using RKHS method.(English)Zbl 1264.45012

Summary: Reproducing kernel Hilbert space method is applied to approximate the solution of two-point boundary value problems for fourth-order integro-differential equations. The analytical solution is represented in the form of series in the reproducing kernel space. The $$n$$-term approximation is obtained and is proved to converge to the analytical solution. Moreover, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solutions and its all derivatives up to order four will be applicable. Numerical examples are given to demonstrate the computation efficiency of the presented method. Results obtained by the method indicate the method is simple and effective.

### MSC:

 45J05 Integro-ordinary differential equations 47B32 Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) 34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
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