An efficient numerical approximation for the linear class of Fredholm integro-differential equations based on Cattani's method

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 7, 2011, Pages 2672-2679

  Maleknejad, K ^a   Attary, M ^a  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Cattani's connection coefficients; Fredholm integro differential equations; Numerical treatments; Shannon wavelets approximation

Indexed keywords

FREDHOLM INTEGRAL EQUATIONS; INTEGRODIFFERENTIAL EQUATIONS;

CATTANI CONNECTION COEFFICIENT; CONNECTION COEFFICIENTS; EQUATION BASED; FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS; GENERALISATION; NUMERICAL APPROXIMATIONS; NUMERICAL TREATMENTS; SHANNON WAVELET; SHANNON WAVELET APPROXIMATION; WAVELET APPROXIMATIONS;

NUMERICAL METHODS;

EID: 79951579463     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.09.037     Document Type: Article

References (19)

1. Rashidinia J., Zarebnia M. The numerical solution of integro-differential equation by means of the Sinc method. Appl Math Comput 2007, 188:1124-1130.
2. Maleknejad K., Tavassoli Kajani M. Solving integro-differential equation by using Hybrid Legendre and Block-Pulse functions. Int J Appl Math 2002, 11(1):67-76.
3. Hossieni S.M., Shahmorad S. Tau numerical solution of Fredholm integro-differential equations with arbitrary polynomial bases. Appl Math Model 2003, 27:145-154.
4. Hossieni S.M., Shahmorad S. Numerical piecewise approximate solution of Fredholm integro-differential equations by the Tau method. Appl Math Model 2005, 29:1005-1021.
5. Pour-Mahmoud J., Rahimi-Ardebili M.Y., Shahmorad S. Numerical solution of Volterra integro-differential equations by the Tau method with the Chebyshev and Legendre bases. Appl Math Comput 2005, 170:314-338.
6. Jaradat H., Alsayyed O., Al-shara S. Numerical solution of linear integro-differential equations. J Math Stat 2008, 4(4):250-254.
7. Maleknejad K., Hadizadeh M. A new computational method for Volterra-Fredholm integral equations. Comput Math Appl 1999, 38:1-8.
8. Wazwaz A.M., Khuri S.A. A reliable technique for solving the weakly singular second-kind Volterra-type integral equations. Appl Math Comput 1990, 80:287-299.
9. Yalcinbas S. Taylor polynomial solution of nonlinear Volterra-Fredholm integral equations. Appl Math Comput 2002, 127:195-206.
10. Cattani C. Shannon wavelets for the solution of integro-differential equations. Math Probl Eng 2010, 1-22.
11. Deriaz E. Shannon wavelet approximation of linear differential operators. Inst Math Pol Acad Sci 2007, 676.
12. Cattani C. Shannon wavelets theory. Math Probl Eng 2008, 1-24.
13. Cattani C. Connection coefficients of Shannon wavelets. Math Model Anal 2006, 11(2):117-132.
14. Cattani C. Harmonic wavelets towards the solution of nonlinear PDE. Comput Math Appl 2005, 50:1191-1210.
15. Latto A., Resnikoff H.L., Tenenbaum E. The evaluation of connection coefficients of compactly supported wavelets. Proceedings of the French-USA workshop on wavelets and turbulence 1992, 78-89. Springer, New York. Y. Maday (Ed.).
16. Cattani C. Harmonic wavelet solution of poisson's problem. Balkan J Geom Appl 2008, 13(1):27-37.
17. Romine CH, Peyton BW. Computing connection coefficients of compactly supported wavelets on bounded intervals. Tech. Rep. ORNL/TM-13413, Oak Ridge, Computer Science and Mathematical Division, Mathematical Sciences Section, 1997.
18. Pandey J.N. Shannon wavelet series expansion of a class of generalized functions. J Wavelet Appl 2007, 1(1):65-81.
19. Maleknejad K., Mahmoudi Y. Numerical solution of integro-differential equation by using Hybrid Taylor and Block-Pulse functions. J Math Sci 2003, 9(2):203-213.