SOLVING INTEGRO-DIFFERENTIAL EQUATIONS USING EXPONENTIALLY FITTED COLLOCATION APPROXIMATE TECHNIQUE(EFCAT)

Abstract

In this paper, both linear Volterra and Fredholm integro-differential equations are considered. We
propose  and  implement Exponentially  Fitted Collocation  Approximate Technique  (EFCAT) to  solve
these types of equations. The collocated perturbed Integro-differential equations were transformed in
to square matrix form which eventually solved using MAPLE 18 software. In order to investigate the
accuracy of the solution with a finite number of computation length (N=8 and N=10) four examples
were considered. To show the efficiency of the present method, numerical experiments are performed
on some applied problems which have been solved by some existing methods and the numerical solutions
are  compared with available results in the literature  and that of analytical solution. The numerical
results obtain show the simplicity and efficiency of the method.

Keywords

• Volterra and Fredholm integro-differential equations,exponentially fitted collocation approximate technique,analytical solution

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