A NUMERICAL ALGORITHM FOR SINGULAR MULTI-POINT BVPS USING THE REPRODUCING KERNEL METHOD
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In this paper, we construct a complex reproducing kernel space for sin-gular multi-point BVPs, and skillfully obtain reproducing kernel expressions. Then,we transform the problem into an equivalent operator equation, and give a numeri-cal algorithm to provide the approximate solution. The uniform convergence of thisalgorithm is proved, and complexity analysis is done. Lastly, we show the validityand feasibility of the numerical algorithm by two numerical examples.
Abstract
In this paper, we construct a complex reproducing kernel space for sin-gular multi-point BVPs, and skillfully obtain reproducing kernel expressions. Then,we transform the problem into an equivalent operator equation, and give a numeri-cal algorithm to provide the approximate solution. The uniform convergence of thisalgorithm is proved, and complexity analysis is done. Lastly, we show the validityand feasibility of the numerical algorithm by two numerical examples.
참고문헌 (15)
- F. Wong, "Positice solution for singular boundary value problems", Comput. Math. Appl, 32(9), pp.41~49 (1996)
- P. Kelevedjiev:, "Existence of positice solution to a singular second order boundary value problem", Nonlinear Anal, 50, pp.1107~1118 (2002)
- X. Xu, "A note on singular nonlinear boundary value problems", J. Math. Anal. Appl, 293, pp.108~124 (2004)
- Y. Liu, "Existence and uniqueness of positice solution for singular boundary value problem", Comput. Math. Appl, 50, pp.133~143 (2005)
- K. Al-Khaled, "Theory and computation in singular boundary value problems", Chaos Solitons Fractals, 33, pp.678~684 (2007)
- L.U. Junfeng, "Variational iteration method for solving two-point boundary value prob-lems", J. Comput. Appl. Math, 207, pp.92~101 (2007)
- A.S.V, "Cubic spline for a class of two-point boundary value problems", Appl. Math. Comput, 207, pp.733~740 (2005)
- John R. Graef, "Necessary and su±cient conditions for the existence of symmetric positive solutions of multi-point boundary value problems", Nonlinear Anal, 68, pp.1529~1552 (2008)
- Qingkai Kong, "Positive solutions of even order system periodic boundary value problems", Nonlinear Anal, 72, pp.1778~1791 (2010)
- Siraj-ul-Islam, "Nonpolynomial spline approach to the solution of a system of second-order boundary-value problems", Appl. Math. Comput, 173, pp.1208~1218 (2006)
- Siraj-ul-Islam, "The numerical solution of second-order boundary-value problems by collocation method with the Haar wavelets", Math. Comput. Modelling, 52, pp.1577~1590 (2010)
- J. Caballero, "Positive solutions for a class of singular fractional boundary value problems", Comput. Math. Appl, 62, pp.1325~1332 (2011)
- Tieshan He, "Existence and multi-plicity of positive solutions for nonlinear boundary value problems with a parameter", Comput. Math. Appl, 61, pp.3355~3363 (2011)
- A.S.V. Ravi Kanth, "Solution of singular two-point boundary value prob-lems using differential transformation method", Phys. Lett. A, 372, pp.4671~4673 (2008)
- Boying Wu, "Application of the reproducing kernel space" (2012), Science Press