Institute for Numerical and Computational Analysis Dublin, Ireland An adaptive uniformly convergent numerical method for a semilinear singular perturbation problem
نویسندگان
چکیده
A singularly perturbed semilinear two point boundary value problem is considered, without any restriction on its turning points. A difference scheme is presented for solving this problem on an arbitrary locally quasiuniform mesh. It is shown that the solution of the scheme is first order accurate, uniformly in the perturbation parameter, in a discrete L1 norm. Numerical results are presented for an adaptive method based on the scheme.
منابع مشابه
A class of singularly perturbed semilinear differential equations with interior layers
In this paper singularly perturbed semilinear differential equations with a discontinuous source term are examined. A numerical method is constructed for these problems which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented that validate the theoretical results.
متن کاملSingularly perturbed differential equations with discontinuous source terms . ∗
In this paper a singularly perturbed reaction-diffusion equation with a discontinuous source term is examined. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented which validate the theoretical results.
متن کاملSingularly perturbed convection diffusion problems with boundary and weak interior layers
In this paper a singularly perturbed convection–diffusion equation with a discontinuous source term is examined. Boundary and weak interior layers appear in the solution. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter.
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 کاملHigh order fitted operator numerical method for self-adjoint singular perturbation problems
We consider self-adjoint singularly perturbed two-point boundary value problems in conservation form. Highest possible order of uniform convergence for such problems achieved hitherto, via fitted operator methods, was one (see, e.g., [Doolan et al. Uniform numerical methods for problems with initial and boundary layers, Boole Press, Dublin, 1980], p. 121]). Reducing the original problem into th...
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 1987