Regularization of A Singularly Perturbed Elliptic PDE
نویسنده
چکیده
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 the original are shown for such equations even though the equation involves an unbounded operator. Key-Words: Singular Perturbation, Elliptic PDE, Regularization
منابع مشابه
Ray Solution of a Singularly Perturbed Elliptic PDE with Applications to Communications Networks
We analyze a second order, linear, elliptic PDE with mixed boundary conditions. This problem arose as a limiting case of a Markovmodulated queueing model for data handling switches in communications networks. We use singular perturbation methods to analyze the problem. In particular we use the ray method to solve the PDE in the e-mail: [email protected] e-mail: [email protected]
متن کاملA quasi-optimal error estimate for a discrete singularly perturbed approximation to the prescribed curvature problem
Solutions of the so-called prescribed curvature problem minA⊆Ω PΩ(A)− ∫ A g(x), g being the curvature field, are approximated via a singularly perturbed elliptic PDE of bistable type. For nondegenerate relative minimizers A ⊂⊂ Ω we prove an O( 2| log |2) error estimate (where stands for the perturbation parameter), and show that this estimate is quasi-optimal. The proof is based on the construc...
متن کاملNumerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type
In this paper, we have proposed a numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided in...
متن کاملA hybrid method for singularly perturbed delay boundary value problems exhibiting a right boundary layer
The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed diffe...
متن کاملAn efficient numerical method for singularly perturbed second order ordinary differential equation
In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004