Modified Algorithms for solving Volterra-Fredholm Integral Equations

In this book, we proposed new numerical algorithms for solving linear Volterra-Fredholm integral equation of the second kind. The numerical solution of this equation is obtained by three ways: The First, using quadrature methods include "trapezoidal rule, Simpson's 1/3 rule, Simpson's 3/8 rule, Boole's rule, and Weddle's rule ". The second, Richardson's extrapolation method is used to modify the results that obtained by using trapezoidal rule. Finally, Lagrange polynomials include "original Lagrange polynomial, modified Lagrange polynomial, and barycentric Lagrange polynomial" are used. Moreover, several examples are presented to demonstrate the applicability, accuracy and efficiency of those methods. Also, for Lagrange polynomials the convergence analysis contains "The error and the bounds of error" are discussed. Additionally, the condition number is obtained. At the end of each method we give new algorithms and programs are developed and written in MATLAB\ R2012a