A Liouville-Green (or WKB) asymptotic approximation theory is developed for the class of linear second-order matrix differential equations Y''= [f(t) A + G(t)] Y on [a, + infinity), where A and G(t) are matrices and f(t) is scalar. This includes the case of an ''asymptotically constant'' (not necessarily diagonalizable) coefficient, A (when f(t)=1). An explicit representation for a basis of the right-module of solutions is given, and precise computable bounds for the error terms are provided. The double asymptotic nature with respect to both, t and some parameter entering the matrix coefficient, is also shown. Several examples, some concerning semi-discretized wave and convection-diffusion equations, are given.
SPIGLER R, & M. VIANELLO (2007). Liouville-Green asymptotic approximation for a class of matrix differential equations and semi-discretized partial differential equations. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 325, 69-89.
Titolo: | Liouville-Green asymptotic approximation for a class of matrix differential equations and semi-discretized partial differential equations | |
Autori: | ||
Data di pubblicazione: | 2007 | |
Rivista: | ||
Citazione: | SPIGLER R, & M. VIANELLO (2007). Liouville-Green asymptotic approximation for a class of matrix differential equations and semi-discretized partial differential equations. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 325, 69-89. | |
Abstract: | A Liouville-Green (or WKB) asymptotic approximation theory is developed for the class of linear second-order matrix differential equations Y''= [f(t) A + G(t)] Y on [a, + infinity), where A and G(t) are matrices and f(t) is scalar. This includes the case of an ''asymptotically constant'' (not necessarily diagonalizable) coefficient, A (when f(t)=1). An explicit representation for a basis of the right-module of solutions is given, and precise computable bounds for the error terms are provided. The double asymptotic nature with respect to both, t and some parameter entering the matrix coefficient, is also shown. Several examples, some concerning semi-discretized wave and convection-diffusion equations, are given. | |
Handle: | http://hdl.handle.net/11590/142416 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |