The solution of integral equations in Chebyshev series

Author:
R. E. Scraton

Journal:
Math. Comp. **23** (1969), 837-844

MSC:
Primary 65.75

DOI:
https://doi.org/10.1090/S0025-5718-1969-0260224-4

MathSciNet review:
0260224

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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.

**[1]**D. L. Elliott, ``The numerical solution of integral equations using Chebyshev polynomials,''*J. Austral. Math. Soc.*, v. 1, 1959-60, pp. 344-356. MR**23**#B1131. MR**0128087 (23:B1131)****[2]**D. L. Elliott ``A Chebyshev series method for the numerical solution of Fredholm integral equations,''*Comput. J.*, v. 6, 1963-64, pp. 102-111. MR**27**#5386. MR**0155452 (27:5386)****[3]**R. E. Scraton, ``The solution of linear differential equations in Chebyshev series,''*Comput. J.*, v. 8, 1965, pp. 57-61. MR**32**#603. MR**0183121 (32:603)****[4]***Modern Computing Methods*, National Physical Laboratory, Notes on Applied Science no. 16, H.M.S.O., London, 1961. MR**22**#8637. MR**0088783 (19:579e)****[5]**J. H. Wilkinson,*The Algebraic Eigenvalue Problem*, Clarendon Press, Oxford, 1965. MR**32**#1894. MR**0184422 (32:1894)**

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DOI:
https://doi.org/10.1090/S0025-5718-1969-0260224-4

Article copyright:
© Copyright 1969
American Mathematical Society