Topic
Method of matched asymptotic expansions
About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.
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TL;DR: RKHSM (Reproducing Kernel Hilbert Space Method) without Gram–Schmidt orthogonalization process, is considered and the domain of the singularly perturbed differential-difference equation is decompose into two subintervals.
16 citations
TL;DR: In this article, it was shown that the effects of large bulk viscosity are non-negligible when the ratio of bulk to shear viscosities is of the order of the square root of the Reynolds number.
Abstract: We examine the inviscid and boundary-layer approximations in fluids having bulk viscosities which are large compared with their shear viscosities for three-dimensional steady flows over rigid bodies. We examine the first-order corrections to the classical lowest-order inviscid and laminar boundary-layer flows using the method of matched asymptotic expansions. It is shown that the effects of large bulk viscosity are non-negligible when the ratio of bulk to shear viscosity is of the order of the square root of the Reynolds number. The first-order outer flow is seen to be rotational, non-isentropic and viscous but nevertheless slips at the inner boundary. First-order corrections to the boundary-layer flow include a variation of the thermodynamic pressure across the boundary layer and terms interpreted as heat sources in the energy equation. The latter results are a generalization and verification of the predictions of Emanuel (Phys. Fluids A, vol. 4, 1992, pp. 491–495).
16 citations
TL;DR: The contractivity and asymptotic stability results of the solution to Volterra partial functional differential equations and delay integro-differential equations of “Hale’s” form are obtained respectively and form the basis for obtaining insight into the analogous properties of their numerical solutions.
16 citations
TL;DR: In this paper, asymptotic expansions are derived as power series in a small coefficient entering a nonlinear multiplicative noise and a deterministic driving term in a non-linear evolution equation.
16 citations
TL;DR: Two simple pairs of asymptotic expansions in terms of Hermite functions are obtained for the solutions of the ellipsoidal wave equation in this article, where the Hermite function is defined as a function of the wave equation.
Abstract: Two simple pairs of asymptotic expansions in terms of Hermite functions are obtained for the solutions of the ellipsoidal wave equation.
16 citations