An Efficient Hybrid Algorithm for the Computation of Second-Order Fredholm Integro-Differential Equations (original) (raw)
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FULafia Journal of Science and Technology, 2019
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.
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