A new algorithm for higher order integro-differential equations

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• 作者：Majid Khan (1)
  
  1. Department of Sciences and Humanities ; National University of Computer & Emerging Sciences ; Islamabad ; Pakistan
  
• 关键词：Modified Laplace decomposition method ; Fifth order integro ; differential equations ; Linear and nonlinear problems ; 45J05 ; 34K10 ; 34K05
• 刊名：Afrika Matematika
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：26
• 期：1-2
• 页码：247-255
• 全文大小：132 KB
• 参考文献：1. Kythe, P.K., Puri, P.: Computational methods for linear integral equations. University of New Orleans, New Orleans (1992)
  2. Wazwaz, A.M.: A comparison study between the modified decomposition method and the traditional methods. Appl. Math. Comput. pp 1703鈥?712 (2006)
  3. Zhao, J., Corless, R.M.: Compact finite difference method for integro-differential equations. Appl. Math. Comput. 177, 271鈥?88 (2006) CrossRef
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  5. Mohammad Hosseinia, S., Shahmoradb, S.: Numerical piecewise approximate solution of Fredholm integro-differential equations by the Tau method. Appl. Math. Model. 29, 1005鈥?021 (2005) CrossRef
  6. Avudainayagam, A., Vani, C.: Wavelet-Galerkin method for integro-differential equations. Appl. Numer. Math. 32, 247鈥?54 (2000) 8-9274(99)00026-4" target="_blank" title="It opens in new window">CrossRef
  7. Rashed, M.T.: Lagrange interpolation to compute the numerical solutions of differential, integral and integro-differential equations. Appl. Math. Comput. 151, 869鈥?78 (2004) CrossRef
  8. Hosseini, S.M., Shahmorad, S.: Tau numerical solution of Fredholm integro-differential equations with arbitrary polynomial bases. Appl. Math. Model. 27, 145鈥?54 (2003) CrossRef
  9. El-Sayed, S.M., Abdel-Aziz, M.R.: A comparison of Adomian鈥檚 decomposition method and Wavelet-Galerkin method for integro-differential equations. Appl. Math. Comput. 136, 151鈥?59 (2003) CrossRef
  10. Wazwaz, A.M.: A reliable algorithm for solving boundary value problems for higher-order integro-differential equations. Appl. Math. Comput. 118, 327鈥?42 (2001) 8" target="_blank" title="It opens in new window">CrossRef
  11. Hashim, I.: Adomian decomposition method for solving BVPs for fourth-order integro-differential equations. J. Comput. Appl. Math. 193, 658鈥?64 (2006) CrossRef
  12. Yildirim, A.: Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method. Comput. Math. Appl. 56, 3175鈥?180 (2008) 8.07.020" target="_blank" title="It opens in new window">CrossRef
  13. Maleknejad, K., Mahmoudi, Y.: Taylor polynomial solution of high-order nonlinear Volterra Fredholm integro-differential equations. Appl. Math. Comput. 145, 641鈥?53 (2003) 8" target="_blank" title="It opens in new window">CrossRef
  14. Maleknejad, K., Mirzaee, F., Abbasbandy, S.: Solving linear integro-differential equations system by using rationalized Haar function method. Appl. Math. Comput. 155, 317鈥?28 (2005) 8-1" target="_blank" title="It opens in new window">CrossRef
  15. Arikoglu, A., Ozkol, I.: Solution of boundary value problems for integro-differential equations by using differential transform method. Appl. Math. Comput. 168, 1145鈥?158 (2005) CrossRef
  16. Sweilam, N.H.: Fourth order integro-differential equations using variational iteration method. Comput. Math. Appl. 54, 1086鈥?091 (2007) CrossRef
  17. He, J.H.: Variational iteration method: new development and applications. Comput. Math. Appl. 54, 881鈥?94 (2007) 83" target="_blank" title="It opens in new window">CrossRef
  18. Khan, M., Hussain, M.: Application of Laplace decomposition method on semi-infinite domain. Numer. Algorithms 56, 211鈥?18 (2011) 82-0" target="_blank" title="It opens in new window">CrossRef
  19. Khan, M., Gondal, M.A.: A new analytical solution procedure for nonlinear integral equations. Math. Comput. Model. 55, 1892鈥?897 (2012) CrossRef
  20. Khan, M., Gondal, M.A.: A reliable treatment of Abel鈥檚 second kind singular integral equations. Appl. Math. Lett. 25, 1666鈥?670 (2012) CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668

文摘

A new modified Laplace decomposition is established for approximate solution of fifth order integro-differential equations. The approximate numerical results confirm the reliability and efficiency of the proposed new algorithm. The proposed mathematical technique is verified on linear and nonlinear problems.