# 一类Fredholm积分微分方程边值问题的数值方法Numerical Algorithm for a Class of Fredholm Integro-Differential Boundary Value Problems

• 全文下载: PDF(361KB)    PP.644-650   DOI: 10.12677/AAM.2017.64075
• 下载量: 921  浏览量: 2,115   科研立项经费支持

This paper discusses the numerical method for a class of Fredholm integro-differential boundary value problems. By constructing the reproducing kernel space which satisfies the boundary condi-tions, the simple reproducing kernel numerical approximate method is established. The paper describes both the exact solution obtained in the form of series and the approximate solution ob-tained by truncating the series representation of the exact solution. Error estimation of the method was discussed. The results of numerical simulation demonstrate the validity of the method in the paper.

  Jaradat, H., Alsayyed, O., and Al-Shara, S. (2008) Numerical Solution of Linear Integro-Differential Equations. Journal of Mathe-matics and Statistics, 4, 250-254. https://doi.org/10.3844/jmssp.2008.250.254  Saadatmandia, A. and Dehghan, M. (2010) Numerical Solution of the Higher-Order Linear Fredholm Integro Diffrential-Difference Equation with Variable Coefficients. Applied Mathematics and Computation, 59, 2996-3004. https://doi.org/10.1016/j.camwa.2010.02.018  Agarwal, R. (1986) Boundary Value Problems for High Order Differential Equations. World Scientific, Singapore.  Bildik, N., Konuralp, A. and Yalçinbas S. (2010) Comparison of Legendre Polynomial Approximation and Variational Iteration Method for the Solutions of General Linear Fredholm Integro-Differential Equations. Applied Mathematics and Computation, 59, 1909-1917. https://doi.org/10.1016/j.camwa.2009.06.022  Hashim, I. (2006) Adomian Decomposition Method for Solving BVPs for Fourth-Order Integro-Differential Equations. Journal of Computational and Applied Mathematics, 193, 658-664. https://doi.org/10.1016/j.cam.2005.05.034  Hosseini, S. and Shahmorad, S. (2003) Tau Numerical Solution of Fredholm Integro-Differential Equations with Arbitrary Polynomial Bases. Applied Mathematical Modelling, 27, 145-154. https://doi.org/10.1016/S0307-904X(02)00099-9  Li, X.Y. and Wu, B.Y. (2015) Approximate Analytical Solutions of Nonlocal Fractional Boundary Value Problems. Applied Mathematical Modelling, 39, 1717-1724. https://doi.org/10.1016/j.apm.2014.09.035  Geng, F.Z. and Qian, S.P. (2014) A New Reproducing Kernel Method for Linear Nonlocal Boundary Value Problems. Applied Mathematics and Computation, 248, 421-425. https://doi.org/10.1016/j.amc.2014.10.002  Wu, B.Y., Guo, L.H. and Zhang, D.Z. (2015) A Novel Method for Solving a Class of Second Order Nonlinear Differential Equations with Finitely Many Singularities. Applied Mathematics Letters, 41, 1-6.  Wu, B.Y. and Li, X.Y. (2010) Application of Reproducing Kernel Method to Third Order Three-point Boundary Value Problems. Applied Mathematics and Computation, 217, 3425-3428. https://doi.org/10.1016/j.amc.2010.09.009  Zhou, Y.F., Cui, M.G. and Lin, Y.Z. (2010) A Computational Method for Nonlinear 2m-th Order Boundary Value Problems. Mathematical Mod-elling and Analysis, 15, 571-586. https://doi.org/10.3846/1392-6292.2010.15.571-586  周永芳. 若干微分方程非局部边值问题的一种数值方法[D]: [博士学位论文]. 哈尔滨: 哈尔滨工业大学, 2011.