A numerical solution to nonlinear second order three-point boundary value problems in the reproducing kernel space
In this paper, a new numerical algorithm is provided to solve nonlinear three-point boundary value problems in a very favorable reproducing kernel space which satisfies all boundary conditions. Its reproducing kernel function is discussed in detail. We also prove that the approximate solution and it...
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| Published in | Applied mathematics and computation Vol. 218; no. 14; pp. 7362 - 7368 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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15.03.2012
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| Abstract | In this paper, a new numerical algorithm is provided to solve nonlinear three-point boundary value problems in a very favorable reproducing kernel space which satisfies all boundary conditions. Its reproducing kernel function is discussed in detail. We also prove that the approximate solution and its first and second order derivatives all converge uniformly. The numerical experiments show that the algorithm is quite accurate and efficient for solving nonlinear second order three-point boundary value problems. |
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| AbstractList | In this paper, a new numerical algorithm is provided to solve nonlinear three-point boundary value problems in a very favorable reproducing kernel space which satisfies all boundary conditions. Its reproducing kernel function is discussed in detail. We also prove that the approximate solution and its first and second order derivatives all converge uniformly. The numerical experiments show that the algorithm is quite accurate and efficient for solving nonlinear second order three-point boundary value problems. |
| Author | Lin, Yingzhen Cui, Minggen Niu, Jing |
| Author_xml | – sequence: 1 givenname: Yingzhen surname: Lin fullname: Lin, Yingzhen organization: Department of Mathematics, Harbin Institute of Technology at Weihai, Shandong 264209, China – sequence: 2 givenname: Jing surname: Niu fullname: Niu, Jing email: niujing1982@gmail.com organization: Department of Mathematics, Harbin Institute of Technology at Weihai, Shandong 264209, China – sequence: 3 givenname: Minggen surname: Cui fullname: Cui, Minggen organization: Department of Mathematics, Harbin Institute of Technology at Weihai, Shandong 264209, China |
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| Keywords | Nonlinear problems Reproducing kernel function Three-point boundary value conditions Numerical algorithm |
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| SubjectTerms | Algorithms Approximation Boundary value problems Derivatives Kernels Mathematical analysis Mathematical models Nonlinear problems Nonlinearity Numerical algorithm Reproducing kernel function Three-point boundary value conditions |
| Title | A numerical solution to nonlinear second order three-point boundary value problems in the reproducing kernel space |
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