The Boundary Function Method for Singular Perturbed ProblemsSIAM, 01/01/1995 - 234 من الصفحات This is the first book published in English devoted solely to the boundary function method, which is one of the asymptotic methods. This method provides an effective and simple way to obtain asymptotic approximations for the solutions of certain ordinary and partial differential equations containing small parameters in front of the highest derivatives. These equations, called singularly perturbed equations, are often used in modeling. In addition to numerous examples, the book includes discussions on singularly perturbed problems from chemical kinetics and heat conduction, semiconductor device modeling, and mathematical biology. |
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A₁ additional conditions algorithm analogously ao(t ao(x asymptotic approximation asymptotic expansion asymptotic series asymptotic solution boundary conditions boundary function method boundary layer boundary value problem Butuzov 149 c₁ chemical kinetics coefficients consider construct the asymptotic corner boundary functions corresponding defined derivatives domain eigenvalues exponential estimate expression homoclinic orbit II-functions initial condition initial value problem integral interval Kalachev linear Math matrix N₁ notation obtain the equation ordinary differential equations parabolic equations partial differential equations phase plane rectangle reduced equation regular rest point right-hand side satisfy second equation semiconductor separatrix singularly perturbed problems small parameter solution u(x solvability stable manifold subinterval Substituting system of equations theorem transition layer uo(x Vasil'eva and Butuzov vector function vicinity virtue of condition zero zeroth order zeroth-order approximation θρ ди др Эт მა მე მუ