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Numerical solutions for the three-point boundary value problem of nonlinear fractional differential equations. (English) Zbl 1250.65106
Summary: We present an efficient numerical scheme for solving three-point boundary value problems of nonlinear fractional differential equation. The main idea of this method is to establish a favorable reproducing kernel space that satisfies the complex boundary conditions. Based on the properties of the new reproducing kernel space, the approximate solution is obtained by searching least value techniques. Moreover, uniformly convergence and error estimation are provided for our method. Numerical experiments are presented to illustrate the performance of the method and to confirm the theoretical results.
MSC:
65L10Boundary value problems for ODE (numerical methods)
34A08Fractional differential equations
34B15Nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
46E22Hilbert spaces with reproducing kernels
65L20Stability and convergence of numerical methods for ODE
65L70Error bounds (numerical methods for ODE)