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Error Bounds for the Liouville‐Green Approximation to Initial‐Value Problems
Author(s) -
Taylor James G.
Publication year - 1978
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19780581202
Subject(s) - mathematics , value (mathematics) , initial value problem , exponential function , differential equation , class (philosophy) , homogeneous , variable (mathematics) , homogeneous differential equation , approximation error , type (biology) , mathematical analysis , order (exchange) , differential (mechanical device) , computer science , ordinary differential equation , statistics , physics , combinatorics , differential algebraic equation , ecology , finance , artificial intelligence , economics , biology , thermodynamics
New error bounds are developed for the Liouville‐Green approximation for initial‐value problems governed by a single second‐order linear differential equation. The cases of both exponential‐type and also oscillatory solutions are considered. Previous error bounds are sharpened as a consequence of our development of these new error bounds for initial‐value problems. These new results are applied to an important class of linear differential equations arising in military operations research (specifically, variable‐coefficient Lanchester‐type equations of modern warfare for combat between two homogeneous forces).