A phase fitted FiniteDiffr process for DiffrntEqutns in chemistry

Chen, Xiaoping; Simos, Theodore E.

doi:10.1007/s10910-020-01104-7

Cited by 19 publications

(2 citation statements)

References 135 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above equation which is usually linear, have oscillatory or periodic solutions and deserves special attention (see [6,8]). The focus of the numerical solution of the above equation is the subject of extensive research activity over the last two decades (see [14,7,22,20,19,21,3,13,17]). Extensive reviews of the methods developed for the solution of (1) with oscillating behavior can be found in [19,21] and the references therein, Ibrahim and Ikhile [7], as well as [1,13,17].…”

Section: Introductionmentioning

confidence: 99%

“…Shokri and et al [20] developed a new family of multiderivative methods with vanishing phase-lag for the numerical integration of IVPs with oscillating solutions. More recently, [3] introduced phase-fitting for finite difference process for solving IVPs arising in chemistry. Trigonometric fitting technique have also been applied to other types of predictor-corrector (P-C) methods, such as the work in (see [11]), where they developed a general class of trigonometrically-fitted two-step hybrid (TFTSH) method for solving second order IVPs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Trigonometrically-Fitted Fifth Order Four-Step Predictor-Corrector Method for Solving Linear Ordinary Differential Equations with Oscillatory Solutions

Salih¹,

Ismail²

2022

MJMS

View full text Add to dashboard Cite

In this paper, we proposed a trigonometrically-fitted fifth order four-step predictor-corrector method based on the four-step Adams-Bashforth method as predictor and five-step Adams-Moulton method as corrector to solve linear ordinary differential equations with oscillatory solutions. This method is constructed which exactly integrate initial value problems whose solutions can be expressed as linear combinations of the set functions {sin(υx),cos(υx)} with υ ∈ R, where v represents an approximation of the frequency of the problem. The frequency will be used in the method to raise the accuracy of the solution. Stability of the proposed method is examined and the corresponding region of stability is depicted. The new fifth algebraic order trigonometrically-fitted predictor-corrector method is applied to solve the initial value problems whose solutions involved trigonometric functions. Numerical results presented proved that the prospective method is more efficient than the widely used methods for the numerical solution of linear ordinary differential equations with oscillating solutions.

show abstract