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Information Seminar Paper

Title

ON THE NUMERICAL SOLUTION OF NONLINEAR MIXED VOLTERRA-FREDHOLM INTEGRAL EQUATIONS UTILIZING RADIAL BASIS FUNCTIONS WITH POLYNOMIAL PRECISION

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Abstract

 THIS PAPER DESCRIBES A NUMERICAL METHOD FOR SOLVING NONLINEAR MIXED VOLTERRA-FREDHOLM TYPE INTEGRAL EQUATIONS OF THE SECOND KIND. THE PROPOSED METHOD UTILIZES RADIAL BASIS FUNCTIONS (RBFS) WITH POLYNOMIAL PRECISION AS A BASIS IN THE DISCRETE COLLOCATION METHOD. THE RBF TECHNIQUE IS AN EFFECTIVE SCHEME FOR THE APPROXIMATION OF AN UNKNOWN FUNCTION USING A SET OF DISORDERED DATA. THE COMPUTATIONAL METHOD DEVELOPED IN THE CURRENT PAPER DOES NOT REQUIRE ANY BACKGROUND MESH OR CELL STRUCTURES, SO IT IS MESHLESS METHOD. THIS SCHEME REDUCES THE SOLUTION OF THE NONLINEAR MIXED VOLTERRA- FREDHOLM INTEGRAL EQUATION TO THE SOLUTION OF A NONLINEAR SYSTEM OF ALGEBRAIC EQUATIONS. THE PROPOSED METHOD IS EASY TO IMPLEMENT ON COMPUTER AND IS MORE FLEXIBLE FOR MOST CLASSES OF INTEGRAL EQUATIONS. THE VALIDITY AND EFFICIENCY OF THE NEW TECHNIQUE ARE DEMONSTRATED THROUGH A NUMERICAL EXAMPLE.

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