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Hoffman, (2001), Numerical methods for Engineers and Scientists, 2nd ed., mercel Dekker, Inc. Quality parameters investigated for such products have shown that internal microcellular structures were not uniform and durability was also weak. 318 & Berlin and New York, springer-Verlag Abstract: Molding of PVC Air soles are currently produced with the formulations of Resin (25 Kg), DOP/DBP ( 8 8 Kg), CPW (3 Kg), R9 (0.750 Kg), Ivamol (0.500 Kg), Stearic acid (0.500 Kg), Foaming ADC (0.350 Kg), MBR (8kg) and Ca CO3). The behaviour of solution for different degrees (N) of the trial solution is carefully studied and illustrative examples are included to demonstrate the validity and applicability of the techniques. Abstract: In this paper, we consider the solution of first and second order Linear integro-differential by the use of trial solution formulated as Chebyshev form of Fourier cosine series. Brunner,(2004), Collocation methods for Volterra Integral and related Functional Differential equations, Cambridge University Press, Cambridge UK.

Ebadian,(2007), A method for the numerical solution of the integro-differential equations, applied maths and High resolution pictures of the soles have exhibited the uniform polymeric network.

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Nanotechnology: convergence with modern biology and medicine.

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