A numerical algorithm for solving a class of linear nonlocal boundary value problems. (English) Zbl 1201.65130

This paper is aimed at constructing a multipoint reproducing kernel space and giving a simple numerical algorithm to solve the nonlocal boundary value problem: \[ u^{(n)}(x)+ \sum^{n-1}_{i=0} a_i(x) u^{(i)}(x)= f(x),\;u^{(i-1)}(x_j)= b_{ij},\;u(x_{k+1})- u(x_{k+2})= b_n. \] One numerical example is presented.


65L10 Numerical solution of boundary value problems involving ordinary differential equations
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[1] Henderson, Johnny; Kunkel, Curtis J., Uniqueness of solution of linear nonlocal boundary value problems, Appl. Math. Lett., 21, 1053-1056 (2008) · Zbl 1158.34309
[2] Graef, John R.; Webb, J. R.L., Third order boundary value problems with nonlocal boundary conditions, Nonlinear Anal., 71, 1542-1551 (2009) · Zbl 1189.34034
[3] Benchohra, M.; Hamani, S.; Ntouyas, S. K., Boundary value problems for differential equations with fractional order and nonlocal conditions, Nonlinear Anal., 71, 2391-2396 (2009) · Zbl 1198.26007
[4] Eloe, Paul W.; Henderson, Johnny, Uniqueness implies existence and uniqueness conditions for nonlocal boundary value problems for \(n\) th order differential equations, J. Math. Appl., 331, 240-247 (2007) · Zbl 1396.34011
[5] Geng, Fazhan; Cui, Minggen, Solving a nonlinear system of second order boundary value problems, J. Math. Anal. Appl., 327, 1167-1181 (2007) · Zbl 1113.34009
[6] Wang, Wenyan; Cui, Minggen; Bo, Han, A new method for solving of singular two-point boundary value problems, Appl. Math. Comput., 206, 721-727 (2008) · Zbl 1161.65060
[7] Cui, Minggen; Lin, Yingzhen, Nonlinear Numerical Analysis in Reproducing Kernel Hilbert Space (2009), Nova Science Publisher: Nova Science Publisher New York · Zbl 1165.65300
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