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A Combined Renormalization Group‐Multiple Scale Method for Singularly Perturbed Problems
Author(s) -
O'Malley, Jr Robert E.,
Kirkinis Eleftherios
Publication year - 2010
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2009.00475.x
Subject(s) - method of matched asymptotic expansions , mathematics , ordinary differential equation , renormalization group , singular perturbation , variety (cybernetics) , scale (ratio) , boundary value problem , mathematical analysis , matching (statistics) , differential equation , mathematical physics , physics , quantum mechanics , statistics
This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms.