A new method is proposed for the numerical solution of linear mixed Volterra-Fredholm integral equations in one space variable. The proposed numerical algorithm combines the trapezoidal rule, for the integration in time, with piecewise polynomial approximation, for the space discretization. We extend the method to nonlinear mixed Volterra-Fredholm integral equations. Finally, the method is tested on a number of problems and numerical results are given.

EUDML-ID : urn:eudml:doc:287862
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@article{702975,
     title = {Numerical method for the mixed Volterra-Fredholm integral equations using hybrid Legendre functions},
     booktitle = {Application of Mathematics 2015},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics CAS},
     address = {Prague},
     year = {2015},
     pages = {184-193},
     zbl = {06669929},
     url = {http://dml.mathdoc.fr/item/702975}
}

Nemati, S.; Lima, P.; Ordokhani, Y. Numerical method for the mixed Volterra-Fredholm integral equations using hybrid Legendre functions, dans Application of Mathematics 2015, GDML_Books,  (2015), pp. 184-193. http://gdmltest.u-ga.fr/item/702975/