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Numerical method for the mixed Volterra-Fredholm integral equations using hybrid Legendre functions. (English) Zbl 1363.65222

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, November 18–21, 2015. In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Prague: Czech Academy of Sciences, Institute of Mathematics (ISBN 978-80-85823-65-3). 184-193 (2015).
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.
For the entire collection see [Zbl 1329.00187].

MSC:

65R20 Numerical methods for integral equations
45A05 Linear integral equations
45B05 Fredholm integral equations
45D05 Volterra integral equations
45G10 Other nonlinear integral equations
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