Solvability of Runge-Kutta and Block-BVMs Systems Applied to Scalar ODEs

Authors:
G. Di Lena;Felice Iavernaro
Affiliations:
-;-
Venue:
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Year:
2000

Citing 4
Cited 0

Topics in matrix analysis

Topics in matrix analysis
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Solving ordinary differential equations by generalized Adams methods: properties and implementation techniques

Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Block-Boundary Value Methods for the Solution of Ordinary Differential Equations

SIAM Journal on Scientific Computing

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Abstract

A characterization of P0 matrices is reported and used to derive simple necessary and sufficient conditions for the unique solvability of a class of nonlinear systems of equations depending on a parameter. An application to the problem of existence and uniqueness of the solutions of one-step implicit schemes applied to scalar ODEs is also presented.