By James G., Mann Jr., James E., Physics Simmonds
ISBN-10: 0486675513
ISBN-13: 9780486675510
Emphasizing the "why" in addition to the "how," this beneficial and well-written introductory textual content explains tools for acquiring approximate recommendations to mathematical difficulties through exploiting the presence of small, dimensionless parameters. aimed toward undergraduates in engineering and the actual sciences. Preface. Bibliography. Appendixes.
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Additional resources for A First Look at Perturbation Theory 2nd Edition
Example text
In general, a study of the behavior of these roots is not sufficient to infer the behavior of the solution of the DE because 1 . A non-homogeneous term in the DE can give rise to a term in the general solution whose behavior depends only, in part , on the roots of the associated polynomial . 2 . The imposition of initial conditions ( Ie's ) or boundary conditions ( Be's ) may result in the appearance of f in the constants multiplying the homogeneous terms in the general solution . 3 . The domain of interest may depend on f.
G . , a shell by a membrane) , we shall say that such a BVP exhibits a singu larity in the m odel. We can n ow answer, to some extent, the two questions we posed earlier. 6) outside a boundary layer at t = o . For this reason, Ae-t is called the interior contribution t o y et , f) . Second , because there is n o boundary layer near t = 1 , A can be determined from the BC at t = 1 . In the chapters to follow, we shall develop systematic methods for re ducing singular perturbation problems to regular ones.
4. Most importantly, the solution of the DE will be a function of both f and the independent variable, say t, which immediately raises the question of whether certain approximate solution are uniformly accu rate for all values of t in the domain of interest . Fortunately, when f is small , characterizing the f-dependence of the solution of a DE with Ie 's or Be's simplifies. The rest of this book is 39 44 Singular Perturbations in Ordin ary Differential Equations The term e-t / f is called a boundary layer ( or the b oundary layer con tribution to yet , f» because it is significant only in a narrow layer of width O ( f) near the b oun d ary t = o.
A First Look at Perturbation Theory 2nd Edition by James G., Mann Jr., James E., Physics Simmonds
by Donald
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