Indefinite integration of oscillatory functions

• Autorzy: Paweł Keller
• Języki publikacji: EN

Abstrakty

EN

A simple and fast algorithm is presented for evaluating the indefinite integral of an oscillatory function $\int_x^yi f(t) e^{iωt} dt$, -1 ≤ x < y ≤ 1, ω ≠ 0, where the Chebyshev series expansion of the function f is known. The final solution, expressed as a finite Chebyshev series, is obtained by solving a second-order linear difference equation. Because of the nature of the equation special algorithms have to be used to find a satisfactory approximation to the integral.

Słowa kluczowe

EN

indefinite integration; second-order linear difference equation; oscillatory function

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1998-1999
• Tom: 25
• Numer: 3
• Strony: 301-311

Daty

wydano

1998

otrzymano

1997-04-30

Twórcy

autor

Paweł Keller

• Institute of Computer Science, University of Wrocław, Przesmyckiego 20, 51-151 Wrocław, Poland

Bibliografia

• [1] W. Gautschi, Computational aspects of three-term recurrence relations, SIAM Rev. 9 (1967), 24-82.
• [2] W. M. Gentleman, Implementing Clenshaw-Curtis quadrature. II. Computing the cosine transformation, Comm. ACM 15 (1972), 343-346.
• [3] T. Hasegawa and T. Torii, Indefinite integration of oscillatory functions by the Chebyshev series expansion, J. Comput. Appl. Math. 17 (1987), 21-29.
• [4] T. Hasegawa and T. Torii, Application of a modified FFT to product type integration, ibid. 38 (1991), 157-168.
• [5] T. Hasegawa and T. Torii, An algorithm for nondominant solutions of linear second-order inhomogeneous difference equations, Math. Comp. 64 (1995), 1199-1204.
• [6] T. Hasegawa, T. Torii and H. Sugiura, An algorithm based on the FFT for a generalized Chebyshev interpolation, ibid. 54 (1990), 195-210.
• [7] F. W. J. Olver, Numerical solution of second-order linear difference equations, J. Res. Nat. Bur. Standards 71 (B) (1967), 111-129.
• [8] S. Paszkowski, Numerical Applications of Chebyshev Polynomials and Chebyshev Series, PWN, Warszawa, 1975 (in Polish).