Optimal convergence results of piecewise polynomial collocation solutions for integral–algebraic equations of index-3

In this work, we will consider piecewise polynomial collocation methods for a new class of integral–algebraic equations of index-3. An analysis of the global convergence properties of the collocation methods is given and the optimal order of convergence results is established. The performance of the proposed scheme is illustrated by means of two numerical examples and confirm that we can achieve the expected theoretical orders of convergence.