[Show abstract][Hide abstract] ABSTRACT: In this paper, we deal with a system of integral algebraic equations of the Hessenberg type. Using a new index definition, the existence and uniqueness of a solution to this system are studied. The well-known piecewise continuous collocation methods are used to solve this system numerically, and the convergence properties of the perturbed piecewise continuous collocation methods are investigated to obtain the order of convergence for the given numerical methods. Finally, some numerical experiments are provided to support the theoretical results.
International Journal of Applied Mathematics and Computer Science 06/2013; 23(2):341-355. · 1.01 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Sufficient conditions for existence and uniqueness of the solution of the
Volterra integral equations of the first kind with piecewise continuous kernels
are derived in framework of Sobolev-Schwartz distribution theory. The
asymptotic approximation of the parametric family of generalized solutions is
constructed. The method for the solution's regular part refinement is proposed
using the successive approximations method.
[Show abstract][Hide abstract] ABSTRACT: The Volterra integral equations of the first kind with piecewise smooth kernel are considered. Such equations appear in the theory of optimal control of the evolving systems. The existence theorems are proved. The method for constructing approximations of paramet-ric families of solutions of such equations is suggested. The parametric family of solutions is constructed in terms of a logarithmic power asymptotics.
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