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Article

Nemati, S. ; Lima, P. ; Ordokhani, Y.
Numerical method for the mixed Volterra-Fredholm integral equations using hybrid Legendre functions. (English). In: Brandts, J., Korotov, S., Křížek, M., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Application of Mathematics 2015, In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Proceedings. Prague, November 18-21, 2015. Institute of Mathematics CAS, Prague, 2015. pp. 184-193
MSC: 41A30, 65D30, 65R20 | Zbl 06669929
Keywords:
mixed Volterra-Fredholm integral equations; hybrid Legendre functions; piecewise polynomial approximation; trapezoidal method
Summary:
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.
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