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Solving system of generalized non-linear Volterra integro-differential equations

A. Khani|S. Shahmorad
장전수학회 (Jangjeon Mathematical Society)|2012.01|Advanced Studies in Contemporary Mathematics|제22권 제1호|pp. 133-144

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키워드

Volterra Integro-Di erential EquationsMatrix FormsNumerical Solutions
주제분류수학

초록

In this paper, we study a simple new method to nd numerical solution of the System of Non-linear Volterra Functional Integro-Di erential Equations (SNVFIDE) which is a generalization of [1]. To this end, we will present our method based on matrix form of SNVFIDE. Finally accuracy of the method is veri ed by presenting some numerical examples.

Abstract

In this paper, we study a simple new method to nd numerical solution of the System of Non-linear Volterra Functional Integro-Di erential Equations (SNVFIDE) which is a generalization of [1]. To this end, we will present our method based on matrix form of SNVFIDE. Finally accuracy of the method is veri ed by presenting some numerical examples.

참고문헌 (14)

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  3. E. Babolian, "Solving Concrete Examples by Adomian Method", Appl. Math. Comput, 135, pp.161167~ (2003)
  4. T. Badredine, "Convergence of Adomian's method applied to integral equations", Kybernetes, 28(5), pp.557~564 (1999)
  5. Y. Cherruault, "Decomposition methods and a new proof of convergence", Math. Comput. Modelling, 18(12), pp.103~106 (1993)
  6. G. Ebadi, "Numerical Solution of the Non-linear Volterra Integro-Dfferential Equations by the Tau Method", Appl. Math. Comput, 188, pp.1580~1586 (2007)
  7. M. K. EL-Daou, "Iterated solutions of linear operator equations with the Tau method", Math. Comput, 66(217), pp.207~213 (1997)
  8. S. M. Hosseini, "Tau numerical solution of Fredholm integrodi erential equations with arbitrary polynomial bases", Appl. Math. Modelling, 27, pp.145~154 (2003)
  9. K. M. Liu, "The automatic solution to systems of ordinary di erential equations by the Tau method", J. of Computers and Math. with Applic, 38, pp.197~210 (1999)
  10. K. M. Liu, "Numerical solution of ordinary and partial functiondi erential eigenvalue problems with the Tau method", Computing, 41, pp.205~217 (1989)
  11. E.L. Ortiz, "An operational approach to the Tau method for the numerical solution of non-linear di erential equations", Computing, 27, pp.15~25 (1981)
  12. E. L. Ortiz, "On the numerical solution of non-linear and functional di erential equations with the Tau method, In numerical treatment of di erential equations in applications", pp.127~139 (1978), Springer
  13. J. Pour-Mahmoud, "Numerical solution of Volterra integro-di erential equations by the Tau method with the Chebyshev and Legendre bases", Appl. Math. Comput, 170, pp.314~338 (2005)
  14. J. Pour-Mahmoud, "Numerical solution of the system of Fredholm integro-di erential equations by the Tau method", Appl. Math. Comput, 168, pp.465~478 (2005)

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