منابع مشابه
Exponentially Fitted Symplectic Runge-Kutta-Nyström methods
In this work we consider symplectic Runge Kutta Nyström (SRKN) methods with three stages. We construct a fourth order SRKN with constant coefficients and a trigonometrically fitted SRKN method. We apply the new methods on the two-dimentional harmonic oscillator, the Stiefel-Bettis problem and on the computation of the eigenvalues of the Schrödinger equation.
متن کاملExponentially-fitted methods on layer-adapted meshes
In this paper, a new derivation of a uniformly-convergent, second-order method for singularly-perturbed, linear ordinary differential equations based on the freezing of the coefficients of the differential equation, and integration of the resulting equations subject to continuity and smoothness conditions at the nodes, is presented. The derivation presented here is compared with others based on...
متن کاملOn ε-uniform convergence of exponentially fitted methods
Abstract. A class of methods constructed to numerically approximate the solution of two-point singularly perturbed boundary value problems of the form εu + bu + cu = f use exponentials to mimic exponential behavior of the solution in the boundary layer(s). We refer to them as exponentially fitted methods. Such methods are usually exact on polynomials of certain degree and some exponential funct...
متن کاملExponentially fitted methods applied to fourth-order boundary value problems
Fourth-order boundary value problems are solved by means of exponentially-fitted methods of different orders. These methods, which depend on a parameter, can be constructed following a six-step flow chart of Ixaru and Vanden Berghe. Special attention is paid to the expression of the error term and to the choice of the parameter in order to make the error as small as possible. Some numerical exa...
متن کاملOn the Leading Error Term of Exponentially Fitted Numerov Methods
Abstract. Second-order boundary value problems are solved with exponentially-fltted Numerov methods. In order to attribute a value to the free parameter in such a method, we look at the leading term of the local truncation error. By solving the problem in two phases, a value for this parameter can be found such that the tuned method behaves like a sixth order method. Furthermore, guidelines to ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2000
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(00)00462-3