ON THE INFINITE FIELD OF A CLASS OF WEAKLY SINGULAR INTEGRAL EQUATIONS
Keywords:
infinite field, weakly singular, integro-differential equations.DOI:
https://doi.org/10.17654/0972111822002Abstract
In this study, we present infinite field behaviors for a class of integral equations with weakly singular kernels (Abel type) based on the methods for integro-differential equations in paper [1]. This class of integro-differential equations originated from an aeroelasticity problem [2]. After taking derivatives on the integral equations, equations are in the form of integro-differential equations. By separating variables, choosing splines as basis, interchanging the differentiation and integration of the integro-differential parts, we are able to compute the infinite behaviors of solutions by steps and discover that the possible behaviors depend on a specific formation of the initial conditions. We conclude the main result as a theorem.
Received: January 1, 2022
Accepted: February 10, 2022
References
S. Chiang, Numerical methods for solving a class of hybrid weakly singular integro-differential equations, Appl. Math. 8 (2017), 956-966.
J. A. Burns, E. M. Cliff and T. L. Herdman, A state-space model for an aeroelastic system, Proceedings: 22nd IEEE Conference on Decision and Control, 1983, pp. 1074-1077.
J. A. Burns and K. Ito, On well-posedness of solutions to integro-differential equations of neutral-type in weighted -spaces, Differential Integral Equations 8 (1995), 627-646.
F. Kappel and K. P. Zhang, On neutral functional differential equations with nonatomic difference operator, J. Math. Anal. Appl. 113 (1986), 311-343.
S. Chiang, On the numerical solutions of a class of singular integro-differential equations, Chung Hua Journal of Science and Engineering 4(3) (2006), 43-48.
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