Fourth Order Chebyshev Methods with Recurrence Relation
نویسنده
چکیده
Abstract. In this paper, a new family of fourth order Chebyshev methods (also called stabilized methods) is constructed. These methods possess nearly optimal stability regions along the negative real axis and a three-term recurrence relation. The stability properties and the high order make them suitable for large stiff problems, often space discretization of parabolic PDEs. A new code ROCK4 is proposed, illustrated at several examples, and compared to existing programs.
منابع مشابه
A new method based on fourth kind Chebyshev wavelets to a fractional-order model of HIV infection of CD4+T cells
This paper deals with the application of fourth kind Chebyshev wavelets (FKCW) in solving numerically a model of HIV infection of CD4+T cells involving Caputo fractional derivative. The present problem is a system of nonlinear fractional differential equations. The goal is to approximate the solution in the form of FKCW truncated series. To do this, an operational matrix of fractional integrati...
متن کاملRecurrence Relations for Chebyshev - Type Methods ∗
The convergence of new second-order iterative methods are analyzed in Banach spaces by introducing a system of recurrence relations. A system of a priori error bounds for that method is also provided. The methods are defined by using a constant bilinear operator A, instead of the second Fréchet derivative appearing in the defining formula of the Chebyshev method. Numerical evidence that the met...
متن کاملOn the Second Order Differential Equation Satisfied by Perturbed Chebyshev Polynomials
In some applications one is led to consider perturbations of orthogonal polynomials translated by a modification on the first coefficients of the second order recurrence relation satisfied by these polynomials. Moreover, the four Chebyshev families are among the most useful orthogonal sequences due to their exceptional features. Thus, it is important to clarify and explicit the properties of pe...
متن کاملFactorizations and Representations of Second Order Linear Recurrences with Indices in Arithmetic Progressions
In this paper we consider second order recurrences {Vk} and {Un} . We give second order linear recurrences for the sequences {V±kn} and {U±kn}. Using these recurrence relations, we derive relationships between the determinants of certain matrices and these sequences. Further, as generalizations of the earlier results, we give representations and trigonometric factorizations of these sequences b...
متن کاملChebyshev Spectral Collocation Method for Computing Numerical Solution of Telegraph Equation
In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Scientific Computing
دوره 23 شماره
صفحات -
تاریخ انتشار 2002