Numerical solution of integral equations of the fourth kind with higher index using spectral collocation methods

In this paper, we study the orthogonal polynomial collocation methods applied to a particular class of integral equations of thefourth kind(or integral-algebraic equations (IAEs)) with index-3. Sufficient conditions for the existence and uniqueness solutionsof the IAEs of index-3 are given and an ultraspherical polynomials collocation method including the matrix-vector multiplicationrepresentation is proposed for the numerical solution of these systems. Convergence analysis is provided and a numerical exampleis presented with the aim of illustrating the convergence behaviour of the method.

کلیدواژه ها:

Integral-algebraic equations ، Index-3 ، orthogonal polynomial collocation methods ، Error analysis ، Numerical treatment