Advances on collocation based numerical methods for ordinary differential equations and Volterra integral equations. (English) Zbl 1216.65097

Conte, Dajana; D’Ambrosio, Raffaele; Paternoster, Beatrice

Simos, Theodore E. (ed.), Recent advances in computational and applied mathematics. Dordrecht: Springer (ISBN 978-90-481-9980-8/hbk; 978-90-481-9981-5/ebook). 41-66 (2011).

Summary: We present a survey on collocation based methods for the numerical integration of ordinary differential equations and Volterra integral equations, starting from the classical collocation methods, to arrive at the most important modifications appearing in the literature, also considering the multistep case and the usage of a basis of functions other than polynomials.
For the entire collection see [Zbl 1201.65004].

MSC:

65L60	Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65R20	Numerical methods for integral equations
65L05	Numerical methods for initial value problems involving ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems
65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
45D05	Volterra integral equations
45G10	Other nonlinear integral equations

Keywords:

collocation; two-step collocation; Runge-Kutta methods; two-step Runge-Kutta methods; mixed collocation

Software:

rknstabint