Interval methods of Adams-Bashforth type with variable step sizes
نویسندگان
چکیده
منابع مشابه
A Generalization of the Adams-bashforth Method
In this paper, we investigate a generalization of the Adams-Bashforth method by using the Taylor’s series. In case of m-step method, the local truncation error can be expressed in terms of m − 1 coefficients. With an appropriate choice of coefficients, the proposed method has produced much smaller error than the original Adams-Bashforth method. As an application of the generalized Adams-Bashfor...
متن کاملGradient Methods with Adaptive Step-Sizes
Motivated by the superlinear behavior of the Barzilai-Borwein (BB) method for two-dimensional quadratics, we propose two gradient methods which adaptively choose a small step-size or a large step-size at each iteration. The small step-size is primarily used to induce a favorable descent direction for the next iteration, while the large step-size is primarily used to produce a sufficient reducti...
متن کاملFast convergence pirkn-type pc methods with adams-type predictors
This paper discusses predictor-corrector iteration schemes (PC iteration schemes) based on direct collocation-based Runge-Kutta-Nystr??m corrector methods (RKN corrector methods) for solving nonstiff initial-value problems (IVPs) for systems of special second-order differential equations y??(t)=f(y(t)). Our approach is to regard the well-known parallel-iterated RKN methods (PIRKN methods) as PC...
متن کاملExponentially Fitted Variants of the Two-Step Adams-Bashforth Method for the Numerical Integration of Initial Problems
In this paper, we propose new variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods for the numerical integration of ordinary differential equations (ODEs). The methods are constructed geometrically from an exponentially fitted osculating parabola. The accuracy and stability of the proposed variants is discussed and their applicability to some initial value problems is...
متن کاملExponential multistep methods of Adams-type
The paper is concerned with the construction, implementation and numerical analysis of exponential multistep methods. These methods are related to explicit Adams methods but, in contrast to the latter, make direct use of the exponential and related matrix functions of a (possibly rough) linearization of the vector field. This feature enables them to integrate stiff problems explicitly in time. ...
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: Numerical Algorithms
سال: 2019
ISSN: 1017-1398,1572-9265
DOI: 10.1007/s11075-019-00774-y