Tau approximate solution of weakly singular Volterra integral equations

Mathematical and Computer Modelling

Volumn 57, Issue 3-4, 2013, Pages 494-502

  Karimi Vanani, S ^a   Soleymani, F ^a  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Abel's equations; Spectral methods; Tau method; Weakly singular integral equations

Indexed keywords

ABEL'S EQUATION; APPROXIMATE SOLUTION; ARBITRARY POLYNOMIAL; CHEBYSHEV; INTEGRAL PART; LEGENDRE; NUMERICAL EXPERIMENTS; NUMERICAL SOLUTION; POLYNOMIAL SOLUTION; SPECTRAL METHODS; TAU METHOD; VOLTERRA INTEGRAL EQUATIONS; WEAKLY SINGULAR; WEAKLY SINGULAR INTEGRAL EQUATIONS;

INTEGRODIFFERENTIAL EQUATIONS; NUMERICAL METHODS; POLYNOMIALS;

INTEGRAL EQUATIONS;

EID: 84870498937     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2012.07.004     Document Type: Article

References (31)

1. Ortiz E.L., Samara H. An operational approach to the Tau method for the numerical solution of nonlinear differential equations. Computing 1981, 27:15-25.
2. Lanczos C. Trigonometric interpolation of empirical and analytical functions. J. Math. Phys. 1938, 17:123-199.
3. Liu K.M., Ortiz E.L. Eigenvalue problems for singularly perturbed differential equations. Proceedings of the BAIL II Conference 1982, 324-329. Boole Press, Dublin. J.J.H. Miller (Ed.).
4. Vanani S.Karimi, Aminataei A. Tau approximate solution of fractional partial differential equations. Comput. Math. Appl. 2011, 62:1075-1083.
5. Dehcheshmeh S.S., Vanani S.Karimi, Hafshejani J.S. Operational Tau approximation for the Fokker-Planck equation. Chin. Phys. Lett. 2012, 29(4):1-4.
6. Vanani S.Karimi, Aminataei A. Operational Tau approximation for a general class of fractional integro-differential equations. Comput. Math. Appl. 2011, 30(3):655-674.
7. Hafshejani J.Sedeghi, Vanani S.Karimi, Esmaily J. Operational Tau approximation for neutral delay differential systems. J. Appl. Sci. 2011, 11(14):2585-2591.
8. Liu K.M., Ortiz E.L. Approximation of eigenvalues defined by ordinary differential equations with the Tau method. Matrix Pencils 1983, 90-102. Springer, Berlin. B. Kagestrm, A. Ruhe (Eds.).
9. Liu K.M., Ortiz E.L. Tau method approximation of differential eigenvalue problems where the spectral parameter enters nonlinearly. J. Comput. Phys. 1987, 72:299-310.
10. Liu K.M., Ortiz E.L. Numerical solution of ordinary and partial function-differential eigenvalue problems with the Tau method. Computing 1989, 41:205-217. (Wien).
11. Ortiz E.L., Samara H. Numerical solution of differential eigenvalue problems with an operational approach to the Tau method. Computing 1983, 31:95-103.
12. Liu K.M., Ortiz E.L. Numerical solution of eigenvalue problems for partial differential equations with the Tau-lines method. Comput. Math. Appl. B 1986, 12(5-6):1153-1168.
13. Liu K.M., Ortiz E.L., Pun K.S. Numerical solution of Steklov's partial differential equation eigenvalue problem. Computational and Asymptotic Methods for Boundary and Interior Layers III 1984, 244-249. Boole Press, Dublin. J.J.H. Miller (Ed.).
14. Ortiz E.L., Pun K.S. Numerical solution of nonlinear partial differential equations with Tau method. J. Comput. Appl. Math. 1985, 12-13:511-516.
15. Ortiz E.L., Pun K.S. A bi-dimensional Tau-elements method for the numerical solution of nonlinear partial differential equations with an application to Burgers' equation. Comput. Math. Appl. B 1986, 12(5-6):1225-1240.
16. Ortiz E.L., Samara H. Numerical solution of partial differential equations with variable coefficients with an operational approach to the Tau method. Comput. Math. Appl. 1984, 10(1):5-13.
17. EL-Daou M.K., Khajah H.G. Iterated solutions of linear operator equations with the Tau method. Math. Comp. 1997, 66(217):207-213.
18. Hosseini S.M., Shahmorad S. Numerical solution of a class of integro-differential equations by the Tau method with an error estimation. Appl. Math. Comput. 2003, 136:559-570.
19. Teriele H.J. Collocation method for weakly singular second kind Volterra integral equations with non-smooth solution. IMA J. Numer. Anal. 1982, 2:437-449.
20. Brunner H. 1896-1996: one hundred years of Volterra integral equation of the first kind. Appl. Numer. Math. 1997, 24:83-93.
21. Gorenflo R. Computation of rough solution of Abel integral equation. Inverse and Ill-Posed Problems 1987, 195-210. Academic Press, New York. H. Engl, C. Gioetsch (Eds.).
22. Gorenflo R., Vessella S. Abel Integral Equations: Analysis and Applications. Lecture Notes in Mathematics 1991, vol. 1461. Springer, Berlin.
23. Lamm P.K., Eldén L. Numerical solution of first-kind Volterra equations by sequential Tikhonov regularization. SIAM J. Numer. Anal. 1997, 34(4):1432-1450.
24. Mandal B.N., Chakrabarti A. Applied Singular Integral Equations 2011, Science Publishers.
25. Wazwaz A.M. A First Course in Integral Equations 1997, World Scientific Publishing Company, New Jersey.
26. Lardy L.J. A variation of Nystrom's method for Hammerstein equations. J. Integral Equations 1981, 3:43-60.
27. Kumar S., Sloan I.H. A new collocation-type method for Hammerstein integral equations. J. Math. Comput. 1987, 48:123-129.
28. Brunner H. Implicitly linear collocation method for nonlinear Volterra equations. Appl. Numer. Math. 1992, 9:235-247.
29. Guoqiang H. Asymptotic error expansion variation of a collocation method for Volterra Hammerstein equations. Appl. Numer. Math. 1993, 13:357-369.
30. Baratella P., Orsi A.P. A new approach to the numerical solution of weakly singular Volterra integral equations. J. Comput. Appl. Math. 2004, 163:401-418.
31. Liu K.M., Pan C.K. The automatic solution to systems of ordinary differential equations by the Tau method. Comput. Math. Appl. 1999, 38:197-210.