Hafez, R. M.Doha, E. H.Bhrawy, A. H.Baleanu, D.2019-12-222019-12-222017Cited References in Web of Science Core Collection: 521221-146Xhttps://cutt.ly/yrevNswAccession Number: WOS:000401785100006The mixed Volterra-Fredholm integral equations (VFIEs) arise in various physical and biological models. The main purpose of this article is to propose and analyze efficient Bernoulli collocation techniques for numerically solving classes of two-dimensional linear and nonlinear mixed VFIEs. The novel aspect of the technique is that it reduces the problem under consideration to a system of algebraic equations by using the Gauss-Bernoulli nodes. One of the main advantages of the present approach is its superior accuracy. Consequently, good results can be obtained even by using a relatively small number of collocation nodes. In addition, several numerical results are given to illustrate the features of the proposed technique.enUniversity for Volterra-Fredholm integral equationserror analysiscollocation schemesBernoulli-Gauss nodesPARTIAL-DIFFERENTIAL-EQUATIONSDEGENERATE BERNOULLINONLINEAR FREDHOLMMATRIX-METHODPOLYNOMIALSALGORITHMNUMBERSSCHEMEEULERAPPROXIMATIONArticle