Solutions of a class of sixth order boundary value problems using the reproducing kernel space. (English) Zbl 1364.65148

Summary: The approximate solution to a class of sixth order boundary value problems is obtained using the reproducing kernel space method. The numerical procedure is applied on linear and nonlinear boundary value problems. The approach provides the solution in terms of a convergent series with easily computable components. The present method is simple from the computational point of view, resulting in speed and accuracy significant improvements in scientific and engineering applications.It was observed that the errors in absolute values are better than compared (C. H. C. Hussin and A. Kiliçman [Math. Probl. Eng. 2011, Article ID 724927, 19 p. (2011; Zbl 1213.65148)] and M. A. Noor and S. T. Mahyud-Din [Comput. Math. Appl. 55, No. 12, 2953–2972 (2008; Zbl 1142.65386)], A.-M. Wazwaz [Appl. Math. Comput. 118, 311–325 (2001; Zbl 1023.65074)], P. K. Pandey [Int. J. Pure Appl. Math. 76, No. 3, 317–326 (2012; Zbl 1250.65102)]. Furthermore, the nonlinear boundary value problem for the integro-differential equation has been investigated arising in chemical engineering, underground water flow and population dynamics, and other fields of physics and mathematical chemistry. The performance of reproducing kernel functions is shown to be very encouraging by experimental results.


65L10 Numerical solution of boundary value problems involving ordinary differential equations
34K10 Boundary value problems for functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
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