Legendre spectral method for solving integral and integro-differential equations

References

• Abramowitz , M. and Stegun , I.A. 1972 . Handbook of Mathematical Function , Dover Publication .
   Google Scholar
• Black , K. 1997 . A Spectral Technique with a Local Spectral Basis . SIAM J. Sci. Compu , 18 : 355 – 370 .
   Google Scholar
• Clenshaw , C.W. and Curtis , A.R. 1960 . A Method for Numerical Integration on an Automatic Computer . Numer. Math , 2 : 197 – 205 .
   Google Scholar
• EL-Gendi , S.E. 1969 . Chebyshev Solutions of Differential, Integral, and Integro- Differential Equations . Computer J , 12 : 282 – 287 .
   Web of Science ®Google Scholar
• EL-Gindy , T.M. 1977 . “ Numerical Studied in Optimal Control Theory ” . In Ph. D. Thesis , University of Wales .
   Google Scholar
• EI-Kady , M.M. 1994 . “ Numerical Studies for Optimal Control Problems ” . In Ph. D. Thesis , Assuit University .
   Google Scholar
• Fox , L. and Parker , I.B. 1968 . Chebyshev Polynomial in Numerical Analysis , London : Oxford University Press .
   Google Scholar
• Garey , L.E. and Shaw , R.E. 1991 . Algorithm for the Second Order Integro- Differential Equations . J. Computer Math. Applic , 22 ( 3 ) : 27 – 34 .
   Web of Science ®Google Scholar
• Hatziavramidis , D. and Ku , H-C. 1985 . An Integral Chebyshev Expansion Method for Boundary-Value Problems of ODE Type . J. ofComp. and Maths. Appls , 11 ( 3 ) : 581 – 586 .
   Google Scholar
• Kelley , C.T. 1995 . A Fast Multilevel Algorithm for Integral Equations . SIAM Num. Anal , 2 ( 3 ) : 501 – 513 .
   Google Scholar
• Kelley , C.T. and Northrup , J.I. 1988 . A Pointwise Quasi-Newton Method for Integral Equations . SIAM J. of Numerical Analysis , 25 ( 3 ) : 1138 – 1155 .
   Google Scholar
• Kelley , C.T. 1979 . Solution of H-equations by Iteration . SIAM J. of Mathematical Analysis , 10 ( 3 ) : 844 – 849 .
   Google Scholar
• Parter , S.V. and Rothman , E.G. 1995 . Preconditioning Legendre Spectral Collection Approximations to Elliptic Problems . SIAM J. Numerical Analysis , 32 ( 3 ) : 333 – 385 .
   Google Scholar
• Sneddon , I.N. 1980 . Special Function of Mathematical Physics and Chemistry , Long Man Group Limited .
   Google Scholar
• Maday , Y. , Kaber , S. and Tadmor , E. 1993 . Legendre Pseudospectral Viscosity Method for Nonlinear Conservation Laws . SIAM J. Numerical. Analysis , 30 : 321 – 342 .
   Web of Science ®Google Scholar