Piecewise shooting reproducing kernel method for linear singularly perturbed boundary value problems

Abstract In this letter, a new numerical method is proposed for solving second order linear singularly perturbed boundary value problems with left layers. Firstly a piecewise reproducing kernel method is proposed for second order linear singularly perturbed initial value problems. By combining the method and the shooting method, an effective numerical method is then proposed for solving second order linear singularly perturbed boundary value problems. Two numerical examples are used to show the effectiveness of the present method.

[1]  Tasawar Hayat,et al.  Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method , 2015, Soft Computing.

[2]  Xiaona Li,et al.  Using reproducing kernel for solving a class of singularly perturbed problems , 2011, Comput. Math. Appl..

[3]  F. Z. Geng,et al.  Modified reproducing kernel method for singularly perturbed boundary value problems with a delay , 2015 .

[4]  F. Z. Geng,et al.  Reproducing kernel method for singularly perturbed turning point problems having twin boundary layers , 2013, Appl. Math. Lett..

[5]  Yingzhen Lin,et al.  Representation of exact solution for the time-fractional telegraph equation in the reproducing kernel space , 2011 .

[6]  F. Z. Geng.  A numerical algorithm for nonlinear multi-point boundary value problems , 2012, J. Comput. Appl. Math..

[7]  X. Y. Li,et al.  A numerical method for solving distributed order diffusion equations , 2016, Appl. Math. Lett..

[8]  Esmail Babolian,et al.  Some error estimates for solving Volterra integral equations by using the reproducing kernel method , 2015, J. Comput. Appl. Math..

[9]  Saeid Abbasbandy,et al.  A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems , 2015, J. Comput. Appl. Math..

[10]  Masahiro Yamamoto,et al.  Numerical method in reproducing kernel space for an inverse source problem for the fractional diffusion equation , 2013 .

[11]  Maryam Mohammadi,et al.  Solving the generalized regularized long wave equation on the basis of a reproducing kernel space , 2011, J. Comput. Appl. Math..

[12]  Benito M. Chen-Charpentier,et al.  Analysis and Models in Interdisciplinary Mathematics , 2014 .

[13]  M. Ghasemi,et al.  Numerical solution of nonlinear delay differential equations of fractional order in reproducing kernel Hilbert space , 2015, Appl. Math. Comput..

[14]  Mohammed Al-Smadi,et al.  Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method , 2013, Appl. Math. Comput..

[15]  Masahiro Yamamoto,et al.  Inverse heat problem of determining time-dependent source parameter in reproducing kernel space , 2013 .

[16]  Minggen Cui,et al.  Nonlinear Numerical Analysis in Reproducing Kernel Space , 2009 .

[17]  Boying Wu,et al.  A continuous method for nonlocal functional differential equations with delayed or advanced arguments , 2014 .

[18]  Manoj Kumar,et al.  A boundary value approach for a class of linear singularly perturbed boundary value problems , 2009, Adv. Eng. Softw..

[19]  A. Akgül.  Numerical Solution of Seventh-Order Boundary Value Problems by a Novel Method , 2014 .

[20]  Peng Liu,et al.  Data regularization using Gaussian beams decomposition and sparse norms , 2013 .

[21]  Fazhan Geng,et al.  A novel method for solving a class of singularly perturbed boundary value problems based on reproducing kernel method , 2011, Appl. Math. Comput..

[22]  S. Li,et al.  A numerical method for singularly perturbed turning point problems with an interior layer , 2014, J. Comput. Appl. Math..

[23]  F. Z. Geng,et al.  Fitted reproducing kernel method for singularly perturbed delay initial value problems , 2016, Appl. Math. Comput..

[24]  Omar Abu Arqub,et al.  Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations , 2017, Neural Computing and Applications.

[25]  Fazhan Geng,et al.  Solving a nonlinear system of second order boundary value problems , 2007 .

[26]  F. Z. Geng,et al.  Piecewise reproducing kernel method for singularly perturbed delay initial value problems , 2014, Appl. Math. Lett..

[27]  X. Y. Li,et al.  Error estimation for the reproducing kernel method to solve linear boundary value problems , 2013, J. Comput. Appl. Math..