Abstract
In this paper, we deal with a system of linear and nonlinear integral algebraic equations (IAEs) of Hessenberg type. Convergence analysis of the discontinuous collocation methods is investigated for the large class of IAEs based on the new definitions. Finally, some numerical experiments are provided to support the theoretical results.
Highlights
IntroductionWhere matrix A ∈ C(I, Rr×r), functions f ∈ C(I, Rr) and k ∈ C(D, Rr×r) with D := {(t, s) : 0 ≤ s ≤ t ≤ T }
Consider the system of integral equations of the form tA(t)y(t) + k(t, s)y(s) ds = f (t), t ∈ I := [0, T ], (1.1)where matrix A ∈ C(I, Rr×r), functions f ∈ C(I, Rr) and k ∈ C(D, Rr×r) with D := {(t, s) : 0 ≤ s ≤ t ≤ T }
We study the numerical properties of integral algebraic equations of Hessenberg type:
Summary
Where matrix A ∈ C(I, Rr×r), functions f ∈ C(I, Rr) and k ∈ C(D, Rr×r) with D := {(t, s) : 0 ≤ s ≤ t ≤ T }. For the sake of simplicity we consider the following first kind system of Volterra integral equations for ν = 1 t k1,1(t, s)y1(s) ds = f1(t) and we suppose that k1,1 is an invertible matrix function of size r × r. The piecewise discontinuous polynomial collocation methods for IAEs with differential index 1 of the form y(t) + K11y(t) + K12z(t) = q1(t), K21y(t) + K22z(t) = q2(t). This paper deals with application of discontinuous piecewise polynomial collocation method on higher index IAEs of Hessenberg form, since there is less investigation on these equations and their analyses are not as easy as the index one IAEs. The sections are organized as follows: In Section 2, we introduce a new definition based on the left index.
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