The solution of integral equations in Chebyshev series
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- by R. E. Scraton PDF
- Math. Comp. 23 (1969), 837-844 Request permission
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
- David Elliott, The numerical solution of integral equations using Chebyshev polynomials, J. Austral. Math. Soc. 1 (1959/1960), 344–356. MR 0128087
- David Elliott, Chebyshev series method for the numerical solution of Fredholm integral equations, Comput. J. 6 (1963/64), 102–111. MR 155452, DOI 10.1093/comjnl/6.1.102
- R. E. Scraton, The solution of linear differential equations in Chebyshev series, Comput. J. 8 (1965), 57–61. MR 183121, DOI 10.1093/comjnl/8.1.57
- Modern computing methods, National Physical Laboratory, Teddington, England; Her Majesty’s Stationery Office, London, 1957. Notes on applied science, no. 16. MR 0088783
- J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
Additional Information
- © Copyright 1969 American Mathematical Society
- 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