On holomorphic regularization of strongly nonlinear singularly perturbed problems
نویسندگان
چکیده
منابع مشابه
Regularization of A Singularly Perturbed Elliptic PDE
In this paper, we consider an elliptic partial differential equation where a small parameter is multiplied with one or both of the second derivatives. Four types of basic spectral regularization methods such as Showalter’s, Tikhonov’s, Lardy’s and Lavrentiev’s are applied to approximate the solution by introducing another large (or small) parameter. Convergence of the regularized solutions to t...
متن کاملNumerical analysis of singularly perturbed nonlinear reaction-diffusion problems
Semilinear reaction-diffusion two-point boundary value problems with multiple solutions are considered. Here the second-order derivative is multiplied by a small positive parameter and consequently these solutions can have boundary or interior layers. A survey is given of the results obtained in our recent investigations into the numerical solution of these problems on layer-adapted meshes.
متن کاملShooting Method for Nonlinear Singularly Perturbed Boundary-value Problems
Asymptotic formulas, as ε → 0, are derived for the solutions of the nonlinear differential equation εu+Q(u) = 0 with boundary conditions u(−1) = u(1) = 0 or u′(−1) = u(1) = 0. The nonlinear term Q(u) behaves like a cubic; it vanishes at s−, 0, s+ and nowhere else in [s−, s+], where s− < 0 < s+. Furthermore, Q (s±) < 0, Q (0) > 0 and the integral of Q on the interval [s−, s+] is zero. Solutions ...
متن کاملRobust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems
Recommended by Donal O'Regan This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.
متن کاملFem for Singularly Perturbed Problems
We consider the numerical approximation of singularly perturbed elliptic boundary value problems over non-smooth domains. We use a decomposition of the solution that contains a smooth part, a corner layer part and a boundary layer part. Explicit guidelines for choosing mesh-degree combinations are given that yield nite element spaces with robust approximation properties. In particular, we const...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ufa Mathematical Journal
سال: 2018
ISSN: 2074-1863,2074-1871
DOI: 10.13108/2018-10-3-35