一种解非线性三阶多点边值问题的数值算法
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摘要
主要研究了一类带有多点边值条件的非线性三阶微分方程的求解方法.利用迭代技巧和再生核(RKM)理论相结合来求解此类问题,同时给出了一些算例来说明方法的有效性.
In this paper, we shall present an algorithm for solving a class of nonlinear thirdorder multi-point boundary value problems. The method is based on an iterative technique and the reproducing kernel method(RKM). Numerical results are shown to illustrate the accuracy of the present method.
In this paper, we shall present an algorithm for solving a class of nonlinear thirdorder multi-point boundary value problems. The method is based on an iterative technique and the reproducing kernel method(RKM). Numerical results are shown to illustrate the accuracy of the present method.
引文
[1]Agarwal R P,Thompson H B and Tisdell C C.Three-point boundary value problems for secondorder discrete equations[J].Computer and Mathematics with Applications,2003,45:1429-1435.
[2]Agarwal R P,and Kiguradze I.On multi-point boundary value problems for linear ordinary differential equations with singularities[J].Journal of Mathematical Analysis and Applications,2004,297:131-151.
[3]Thompson H B,and Tisdell C.Three-point boundary value problems for second-order ordinary differential equation[J].Mathematical and Computer Modelling,2001,34:311-318.
[4]Lepin A Y,and Ponomarev V D,On a positive solution of a three-point boundary value problem[J].Differential Equations,2006,42(2):291-293.
[5]Sun Y P.Positive solutions for third-order three-point nonhomogeneous boundary value problems[J].Applied Mathematics Letters,2009,22(1):45-51.
[6]Sun Y P.Existence of triple positive solutions for a third-order three-point boundary value problem[J].Journal of Computational and Applied Mathematics,2008,221(1):194-201.
[7]Moorti V R G,and Garner J B.Existence and uniqueness theorems for three-point boundary value problems for third order differential equations[J].Journal of Mathematical Analysis and Applications,1979,70(2):370-385.
[8]王兆清,李淑萍.非线性问题的重心插值配点法[M].北京:国防工业出版社,2015.
[9]Srivastava P K,and Kumar M.Numerical treatment of nonlinear third order boundary value problem[J].Applied Mathematics,2011,2:959-964.
[10]Geng F Z.A numerical algorithm for nonlinear multi-point boundary value problems[J].J Comput Appl Math,2012,236:1789-1794.
[11]Cui M G,and Geng F Z.Solving singular two-point boundary value problem in reproducing kernel space[J].Journal of Computational and Applied Mathematics,2007,205:6-15.
[12]Geng F Z,and Cui M G.Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space[J].Applied Mathematics and Computation,2007,192:389-398.
[13]Geng F Z,and Cui M G.Solving singular nonlinear two-point boundary value problems in the reproducing kernel space[J].Journal of the Korean Mathematical Society,2008,45(3):77-87.
[14]Cui M G,and Geng F Z.A computational method for solving one-dimensional variable-coefficient Burgers equation[J].Applied Mathematics and Computation,2007,188:1389-1401.
[15]Cui M G,and Chen Z.The exact solution of nonlinear age-structured population model[J].Nonlinear Analysis:Real World Applications,2007,8:1096-1112.
[16]Li C L,and Cui M G.The exact solution for solving a class nonlinear operator equations in the reproducing kernel space[J].Applied Mathematics and Computation,2003,143(2-3):393-399.
[17]吴勃英,林迎珍.应用型再生核空间[M].北京:科学出版社,2012.
[2]Agarwal R P,and Kiguradze I.On multi-point boundary value problems for linear ordinary differential equations with singularities[J].Journal of Mathematical Analysis and Applications,2004,297:131-151.
[3]Thompson H B,and Tisdell C.Three-point boundary value problems for second-order ordinary differential equation[J].Mathematical and Computer Modelling,2001,34:311-318.
[4]Lepin A Y,and Ponomarev V D,On a positive solution of a three-point boundary value problem[J].Differential Equations,2006,42(2):291-293.
[5]Sun Y P.Positive solutions for third-order three-point nonhomogeneous boundary value problems[J].Applied Mathematics Letters,2009,22(1):45-51.
[6]Sun Y P.Existence of triple positive solutions for a third-order three-point boundary value problem[J].Journal of Computational and Applied Mathematics,2008,221(1):194-201.
[7]Moorti V R G,and Garner J B.Existence and uniqueness theorems for three-point boundary value problems for third order differential equations[J].Journal of Mathematical Analysis and Applications,1979,70(2):370-385.
[8]王兆清,李淑萍.非线性问题的重心插值配点法[M].北京:国防工业出版社,2015.
[9]Srivastava P K,and Kumar M.Numerical treatment of nonlinear third order boundary value problem[J].Applied Mathematics,2011,2:959-964.
[10]Geng F Z.A numerical algorithm for nonlinear multi-point boundary value problems[J].J Comput Appl Math,2012,236:1789-1794.
[11]Cui M G,and Geng F Z.Solving singular two-point boundary value problem in reproducing kernel space[J].Journal of Computational and Applied Mathematics,2007,205:6-15.
[12]Geng F Z,and Cui M G.Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space[J].Applied Mathematics and Computation,2007,192:389-398.
[13]Geng F Z,and Cui M G.Solving singular nonlinear two-point boundary value problems in the reproducing kernel space[J].Journal of the Korean Mathematical Society,2008,45(3):77-87.
[14]Cui M G,and Geng F Z.A computational method for solving one-dimensional variable-coefficient Burgers equation[J].Applied Mathematics and Computation,2007,188:1389-1401.
[15]Cui M G,and Chen Z.The exact solution of nonlinear age-structured population model[J].Nonlinear Analysis:Real World Applications,2007,8:1096-1112.
[16]Li C L,and Cui M G.The exact solution for solving a class nonlinear operator equations in the reproducing kernel space[J].Applied Mathematics and Computation,2003,143(2-3):393-399.
[17]吴勃英,林迎珍.应用型再生核空间[M].北京:科学出版社,2012.