Abstract
A fully discrete version of a piecewise polynomial collocation method based on new collocation points, is constructed to solve nonlinear Volterra-Fredholm integral equations. In this paper, we obtain existence and uniqueness results and analyze the convergence properties of the collocation method when used to approximate smooth solutions of Volterra- Fredholm integral equations.
Highlights
The Volterra integral operators given by :C I C I (2) y t t 0 k1 t, s, y sand Fredholm integral operators given by F :C I C I (3) Fy T 0 k2
A fully discrete version of a piecewise polynomial collocation method based on new collocation points, is constructed to solve nonlinear Volterra-Fredholm integral equations
We discuss existence and uniqueness results and analyze the convergence properties of the collocation method when used to approximate smooth solutions of linear Volterra-Fredholm integral equations and some numerical results are presented in the final section, which support the theoretical results obtained in this paper
Summary
The mentioned equations are characterized by the presence of a linear functional argument and play an important role in explaining many different phenomena They turn out to be fundamental when ordinary differential equations based model fail. Chelyshkov has introduced sequences of polynomials in [1], which are orthogonal over the interval 0,1 with the weight function 1 The polynomials Pmk t have properties, which are analogous to the properties of the classical orthogonal polynomials. We discuss existence and uniqueness results and analyze the convergence properties of the collocation method when used to approximate smooth solutions of linear Volterra-Fredholm integral equations and some numerical results are presented, which support the theoretical results obtained in this paper We discuss existence and uniqueness results and analyze the convergence properties of the collocation method when used to approximate smooth solutions of linear Volterra-Fredholm integral equations and some numerical results are presented in the final section, which support the theoretical results obtained in this paper
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