Numerical solution of three-dimensional Volterra–Fredholm integral equations of the first and second kinds based on Bernstein’s approximation

摘要

A new and efficient method is presented for solving three-dimensional Volterra–Fredholm integral equations of the second kind (3D-VFIEK2), first kind (3D-VFIEK1) and even singular type of these equations. Here, we discuss three-variable Bernstein polynomials and their properties. This method has several advantages in reducing computational burden with good degree of accuracy. Furthermore, we obtain an error bound for this method. Finally, this method is applied to five examples to illustrate the accuracy and implementation of the method and this method is compared to already present methods. Numerical results show that the new method provides more efficient results in comparison with other methods.