Integral equations on the half-line: a modified finite-section approximation
نویسندگان
چکیده
منابع مشابه
Integral Equations on the Half-Line: A Modified Finite-Section Approximation
We consider the approximate solution of integral equations of the form y(t) /if k(t,s)y(s)ds = f(t), where the conditions on k(t,s) are such that kernels of the Wiener-Hopf form k(t, s) = n(t s) are included in the analysis. The finite-section approximation, in which the infinite integral is replaced by }§ for some ß > 0, yields an approximate solution _Vß(t) that is known, under very general c...
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We consider integral equations on the halfline of the form x(s) − ∫∞ 0 k(s, t)x(t) dt = y(s) and the finite section approximation xβ to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e., xβ exists and is uniformly bounded in the space of bounded con...
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An orthogonal system of rational functions is introduced. Some results on rational approximations based on various orthogonal projections and interpolations are established. These results form the mathematical foundation of the related spectral method and pseudospectral method for solving differential equations on the half line. The error estimates of the rational spectral method and rational p...
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Coupled modified nonlinear Schrödinger(CMNLS) equations describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. In this paper, we use the Fokas method to analyze the initialboundary value problem for the CMNLS equations on the half-line. Assume that the solution u(x, t) and v(x, t) of CMNLS equations are exists, and we show that it can be expre...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1986
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1986-0856704-0