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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: Several asymptotic expansions for the gamma function due to Laplace, Ramanujan–Karatsuba, Gosper, Mortici, Nemes and Batir are unify.
28 citations
TL;DR: In this paper, the authors apply the FNDM to obtain approximate numerical solutions for two different types of nonlinear time-fractional systems of partial differential equations, and show that their analytical solutions converge very rapidly to the exact solutions.
Abstract: In this article, we focus our study on finding approximate analytical solutions to systems of nonlinear PDEs using the fractional natural decomposition method (FNDM). We apply the FNDM to obtain approximate numerical solutions for two different types of nonlinear time-fractional systems of partial differential equations. The theoretical analysis of the FNDM is investigated for these systems of equations and is calculated in the explicit form of a power series with easily computable terms. The analysis shows that our analytical solutions converge very rapidly to the exact solutions and the effectiveness of the FNDM is numerically confirmed.
28 citations
TL;DR: In this paper, the asymptotic behavior of solution for the initial boundary value problems of reaction diffusion equations with boundary perturbation is studied using the theory of differential inequalities under suitable conditions.
Abstract: A nonlinear singularly perturbed problems for reaction diffusion equation with boundary perturbation is considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems of reaction diffusion equations is studied using the theory of differential inequalities.
28 citations
TL;DR: In this article, the authors studied the asymptotic behavior of solutions of a mixed inhomogeneous boundary value problem and a spectral Neumann problem in a thin perforated domain with rapidly varying thickness.
Abstract: For a second-order symmetric uniformly elliptic differential operator with rapidly oscillating coefficients, we study the asymptotic behavior of solutions of a mixed inhomogeneous boundary-value problem and a spectral Neumann problem in a thin perforated domain with rapidly varying thickness. We obtain asymptotic estimates for the differences between solutions of the original problems and the corresponding homogenized problems. These results were announced in Dopovidi Akademii Nauk Ukrainy, No. 10, 15‐19 (1991). The new results obtained in the present paper are related to the construction of an asymptotic expansion of a solution of a mixed homogeneous boundary-value problem under additional assumptions of symmetry for the coefficients of the operator and for the thin perforated domain.
28 citations