ON EXACT FINITE DIFFERENCE SCHEME FOR THE COMPUTATION OF SECOND-ORDER FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

Abstract

A special form of Non-Standard Finite Difference Method (NSFDM) called the Exact Finite Difference Scheme (EFDS) for the  computation of second-order Fredholm Integro-differential equation shall be constructed in this research. In carrying out the construction of the method, it was assumed that at any point within the interval of integration, the approximate/numerical solution coincides with the exact/theoretical solution. The analysis of the method was also carried out to show that the second-order Fredholm integro-differential equation that possess solutions also have their corresponding EFDS. The method derived was then applied on some modeled second-order Fredholm integro-differential equations and from the results obtained, it is obvious that the EFDS derived did not exhibit any numerical instabilities. As a matter of fact, the computed solutions of the EFDS are exactly equal to the exact solutions