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

Nedaiasl, K.; Foroush Bastani, A.

Dolomites Res. Notes Approx. 10, Spec. Iss., 118-127 (2017).

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.

MSC:

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