On the numerical approximation of some non-standard Volterra integral equations. (English) Zbl 1372.65351

Summary: The numerical solution of non-standard and nonlinear Volterra integral equations is studied and computationally efficient schemes based on quadrature methods are presented. The numerical methods are of Runge-Kutta and barycentric rational quadrature types. A convergence analysis of the barycentric rational quadrature method is discussed and for the Runge-Kutta method, we analyze numerically its convergence properties. The option pricing application of the proposed equation is discussed and finally some open problems in this field are given.


65R20 Numerical methods for integral equations
45D05 Volterra integral equations
91G60 Numerical methods (including Monte Carlo methods)
91G20 Derivative securities (option pricing, hedging, etc.)
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