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 investigate...

In this paper, we deals with a system of integral algebraic equations of Hessenberg type. Using a new definition of index the existence and uniqueness of solution for 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 t...

In this paper we give a complete analysis of the global convergence and local superconvergence properties of piecewise polynomial collocation for Volterra integral equations with constant delay. This analysis includes continuous collocation-based Volterra-Runge-Kutta methods as well as iterated collocation methods and their discretizations.

We show that various (discrete) methods for the approximate solution of Volterra (and Abel) integral equations of the first kind correspond to some discrete version of the method of (recursive) collocation in the space of (continuous) piecewise polynomials. In a collocation method no distinction has to be made between equations with regular or weakly singular kernels; the regularity or nonregul...

This paper is concerned with collocation methods for one class of impulsive delay differential equations (IDDEs). Some results the convergence, global superconvergence and local are given. We choose a suitable piecewise continuous space to obtain high-order numerical methods. illustrative examples given verify theoretical results.

A collocation-Galerkin method is defined for Poisson's equation on the unit 2 square, using tensor products of continuous piecewise polynomials. Optimal L and Hq orders of convergence are established. This procedure requires fewer quadratures than the corresponding Galerkin procedure. Introduction. The collocation-Galerkin method was first introduced by Diaz [2], [3] for the two-point boundary ...

We consider a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polynomials, where the coe cients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra methods, and numerical results are given.

In this work we present numerical methods for the solution of Fredholm integral equations of the second type for smooth and piecewise smooth surfaces We use a collocation method based on piecewise polynomial interpolation of the solution We consider only collocation methods for which the collocation nodes are interior to each triangular face In Chapter II we give the general framework for collo...

A more careful count of the operations involved in solving the linear system associated with collocation of a two-point boundary value problem using rough splines reverses results recently reported by others in this journal. In addition, it is observed that the use of the technique of "condensation of parameters" can decrease the computer storage required. Furthermore, the use of a particular h...