论文信息 - Implicitly linear collocation methods for nonlinear Volterra equations

Implicitly linear collocation methods for nonlinear Volterra equations

Abstract Recently, Kumar and Sloan introduced a new collocation-type method for numerical solution of Hammerstein integral equations. In the present paper we apply this method (which will be referred to as the implicitly linear collocation method) to nonlinear Volterra integral and integro-differential equations and discuss its connection with the iterated collocation method.

Hermann Brunner | H. Brunner

[1] Ian H. Sloan,et al. A new collocation-type method for Hammerstein integral equations , 1987 .

[2] Sunil Kumar. Superconvergence of a Collocation-type Method for Hummerstein Equations , 1987 .

[3] Hermann Brunner,et al. The Numerical Solution of Nonlinear Volterra Integral Equations of the Second Kind by Collocation and Iterated Collocation Methods , 1987 .

[4] Mahadevan Ganesh,et al. Discrete numerical solvability of Hammerstein integral equations of mixed type , 1989 .

[5] H. Brunner. On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods , 1990 .

[6] H. Brunner. On Implicitly Linear and Iterated Collocation Methods for Hammerstein Integral Equations , 1991 .

[7] H. Brunner,et al. The numerical solution of Volterra equations , 1988 .

[8] Ernst Hairer,et al. Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[9] M. A. Krasnoselʹskii,et al. Geometrical Methods of Nonlinear Analysis , 1984 .

[10] Rossana Vermiglio,et al. Stability Analysis of Runge-Kutta Methods for Volterra Integral Equations of the Second Kind , 1990 .

[11] Sunil Kumar,et al. A discrete collocation-type method for Hammerstein equations , 1988 .