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Title

APPLICATION OF CHEBYSHEV COLLOCATION METHOD FOR NUMERICAL SOLUTION OF VOLTERRA-FREDHOLM EQUATIONS

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Abstract

 IN THIS ARTICLE, THE CHEBYSHEV COLLOCATION METHOD IS PRESENTED FOR THE SOLUTIONS OF VOLTERRA-FREDHOLM INTEGRAL EQUATIONS. THIS METHOD IS BASED ON APPROXIMATING UNKNOWN FUNCTION WITH SHIFTED CHEBYSHEV POLYNOMIALS. THE METHOD IS USING A SIMPLE COMPUTATIONS MANNER TO OBTAIN A QUITE ACCEPTABLE APPROXIMATE SOLUTION. WE ALSO GET AN UPPER BOUND FOR THE ERROR OF THIS ALGORITHM. FINALLY, ONE EXAMPLE IS PRESENTED TO SHOW THE APPLICABILITY OF OUR METHOD WITH COMPARE TO THE FOUR WELL KNOWN ALGORITHMS IN THE LITERATURE.

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