Application of the Finite Differences Methods to Computation of Definite Integrals

Abstract

- It is known that one of the popular methods constructed to solve the scientific and engineering problem is the finite difference method studied beginning from the known and famous scientists as the Newton, Leibniz, Euler and etc. One of the first applications of the finite difference method is defined as the conception of the derivatives for the continuous function. These methods have been successfully used in solving of the differential equations at the present time. But here have investigated the application of the finite-difference methods to compute the definite integrals. Constructed the stable methods with the high order of accuracy which are applied to computation of the definite integrals. Also has been found some connection between the constructed multistep methods, the Gauss and Chebyshev methods. The received here methods have been applied to the computation of the double definite integral. For this aim, here have been investigated the double integrals for the degenerate functions. The advantages of these methods are illustrated by using the known model integral, which has been solved by using the stable method with the degree p=6.