Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

The solution of integral equations in Chebyshev series


Author: R. E. Scraton
Journal: Math. Comp. 23 (1969), 837-844
MSC: Primary 65.75
MathSciNet review: 0260224
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If the solution of an integral equation can be expanded in the form of a Chebyshev series, the equation can be transformed into an infinite set of algebraic equations in which the unknowns are the coefficients of the Chebyshev series. The algebraic equations are solved by standard iterative procedures, in which it is not necessary to determine beforehand how many coefficients are significant. The method is applicable to equations of either Fredholm or Volterra types.


References [Enhancements On Off] (What's this?)

  • [1] David Elliott, The numerical solution of integral equations using Chebyshev polynomials, J. Austral. Math. Soc. 1 (1959/1960), 344–356. MR 0128087
  • [2] David Elliott, Chebyshev series method for the numerical solution of Fredholm integral equations, Comput. J. 6 (1963/1964), 102–111. MR 0155452
  • [3] R. E. Scraton, The solution of linear differential equations in Chebyshev series, Comput. J. 8 (1965), 57–61. MR 0183121
  • [4] Modern computing methods, Notes on applied science, no. 16, National Physical Laboratory, Teddington, England. Her Majesty’s Stationery Office, London, 1957. MR 0088783
  • [5] J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.75

Retrieve articles in all journals with MSC: 65.75


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1969-0260224-4
Article copyright: © Copyright 1969 American Mathematical Society