Applied Mathematics & Information Sciences

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In this paper, under certain conditions, the unique solution of a mixed integral equation (MIE) with a singular kernel in position and a continuous kernel in time, in ( 2+1) dimensional is discussed and obtained in the space L2([a,b]×[c,d])×C[0,T],T < 1. After using a separation technique method, and Product Nystrom Method (PNM), we have a linear algebraic system (LAS) in two- dimensional with time coefficients. The convergence of the unique solution of the LAS is studied. In the end, and with the aid of Maple 18, many applications when a singular term of position kernel takes a logarithmic form and Carleman function are solved numerically. Moreover, the error is computed.

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