Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ERROR REDUCTION FOR HIGHER DERIVATIVES OF CHEBYSHEV COLLOCATION METHOD USING PRECONDITIONSING AND DOMAIN DECOMPOSITION

  • Darvishi, M.T. (Inst.of Mathematics University of Teaccher Education) ;
  • Ghoreishi, F. (Dept. of Mathematics Tarbiat Modarres University Tehran)
  • Published : 1999.06.01

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Abstract

A new preconditioning method is investigated to reduce the roundoff error in computing derivatives using Chebyshev col-location methods(CCM). Using this preconditioning causes ration of roundoff error of preconditioning method and CCm becomes small when N gets large. Also for accuracy enhancement of differentiation we use a domain decomposition approach. Error analysis shows that for this domain decomposition method error reduces proportional to the length of subintervals. Numerical results show that using domain decomposition and preconditioning simultaneously gives super accu-rate approximate values for first derivative of the function and good approximate values for moderately high derivatives.

Keywords

References

  1. J. Comput. Physics v.99 On the Errors Incurred Calculating Derivatives Using Chebyshev Polynomials K.S.Breuer;R.S.Everson
  2. Spectral Method in Fluid Mechanics C.Canuto;A.Quarteroni;M.Y.Hossaini;T.Zang
  3. SIAM J. of Sci. Comput. v.18 no.4 Accuracy Enhancement For Higher Derivatives Using Chebyshev Collocation and A Mapping Technique W.S.Don;A.Solomonoff
  4. SIAM J. of Sci. Comput. v.16 no.4 Accuracy and Speed in Computing the Chebyshev Collocation Derivative W.S.Don;A.Solomonoff
  5. Society for Industrial and Applied Mathematics Numerical analysis of Spectral Methods: Theory and Application D.Gottlieb;S.Orszag
  6. J. Comput. Physics v.104 A Modified Chebyshev Pseudospectral Method with an O(N-¹)Time Step Restriction D.Kosloff;H.Tal-Ezer
  7. A First Course in Numerical Analysis A.Ralston
  8. An Introduction to The Approximation of Functions T.J.Rivlin