A main theorem of spectral relationships for Volterra-Fredholm integral equation of the first kind and its applications

作者：Abdou M A^*; Basseem M

来源：Mathematical Methods in the Applied Sciences, 2010, 33(13): 1523-1531.

DOI：10.1002/mma.1251

• Volterra-Fredholm integral equation
• Chebyshev polynomial
• logarithmic kernel
• linear algebraic system (LAS)

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] x 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.

• 出版日期2010-9-15