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A main theorem of spectral relationships for Volterra–Fredholm integral equation of the first kind and its applications
Author(s) -
Abdou M. A.,
Basseem M.
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1251
Subject(s) - mathematics , fredholm integral equation , kernel (algebra) , integral equation , volterra integral equation , logarithm , term (time) , fredholm theory , mathematical analysis , space (punctuation) , pure mathematics , computer science , physics , quantum mechanics , operating system
This paper is concerned to derive the main theorem of spectral relationships of Volterra–Fredholm integral equation (V‐FIE) of the first kind in the space L 2 [−1,1]× C [0, T ], −1⩽ x ⩽1, 0⩽ t ⩽ T <1. The Fredholm integral (FI) term is considered in position and its kernel takes a logarithmic form multiplying by a continuous function. While Volterra integral (VI) term in time with a positive continuous kernel. Many important special and new cases can be established from the main theorem. Moreover, we use it to solve V‐FIE of the second kind in the same space. The numerical results are computed and the error is calculated using Maple 12. Copyright © 2010 John Wiley & Sons, Ltd.