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This paper provides an effective numerical technique for obtaining the approximate solution of mixed Volterra-Fredholm Integral Equations (VFIEs) of second kind. The VFIEs arise from parabolic boundary value problems, mathematical modelling of the spatio-temporal development of an epidemic, and from various physical and Engineering models. The proposed method is based on the discretization of VFIEs by Bernstein’s approximation. Some results on convergence are also established which suggests that the technique converges to a smooth approximate solution. Its remarkable accuracy properties are finally demonstrated by several examples with graphical representation. [ABSTRACT FROM AUTHOR]