An efficient hybrid method for solving fredholm integral equations using triangular functions

An Improved Numerical Method for Solving Nonlinear Volterra-Fredholm Integral Equations Using Hybrid Functions

This paper presents an effective numerical method for solving a class of nonlinear VolterraFredholm integral equations by using the hybrid functions of Legendre polynomials and block-pulse functions. The proposed method which differs with previous approaches, attemp ts to use the exact forms of known functions in solving the integral equation. So its accuracy appropriately increases and the com...

Solving Second Kind Volterra-Fredholm Integral Equations by Using Triangular Functions (TF) and Dynamical Systems

The method of triangular functions (TF) could be a generalization form of the functions of block-pulse (Bp)‎. ‎The solution of second kind integral equations by using the concept of TF would lead to a nonlinear equations system‎. ‎In this article‎, ‎the obtained nonlinear system has been solved as a dynamical system‎. ‎The solution of the obtained nonlinear system by the dynamical system throug...

A Direct Method for Numerically Solving Integral Equations System Using Orthogonal Triangular Functions

A Projection Method for Solving Nonlinear Volterra-Fredholm Integral Equations using Legendre Hybrid Functions

Since various problems in science and engineering fields can be modeled by nonlinear Volterra-Fredholm integral equations, the main focus of this study is to present an effective numerical method for solving them. This method is based on the hybrid functions of Legendre polynomials and block-pulse functions. By using this approach, a nonlinear Volterra-Fredholm integral equation reduces to a no...

Convergence of an Approach for Solving Fredholm Functional Integral Equations

In this work, we give a product Nyström method for solving a Fredholm functional integral equation (FIE) of the second kind. With this method solving FIE reduce to solving an algebraic system of equations. Then we use some theorems to prove the existence and uniqueness of the system. Finally we investigate the convergence of the method.