Efficient Exponential Fitting Algorithm with Two Fitting Parameters for Oscillation Problems

Öziş, Turgut; Erdoğan, Utku

doi:10.1063/1.3637936

Cited by 2 publications

(3 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(7). Erdogan and Ozis have noted that, while their scheme improves truncation errors, it is not well defined for applying to problems of the sort They have tackled this issue for one application of this form in [8]; however, our goal is to create a more general NSFD method. Thus, in this section, we present our extension of Erdogan and Ozis's method for vector problems.…”

Section: An Nsfd Scheme Applied To An Sir Modelmentioning

confidence: 99%

A simple construction of nonstandard finite-difference schemes for small nonlinear systems applied to SIR models

Gurski

2013

Computers & Mathematics with Applications

View full text Add to dashboard Cite

a b s t r a c tWe present a simple mathematical construction for nonstandard finite-difference (NSFD) schemes for small systems of nonlinear differential equations using standard differential equation approximation techniques such as introducing artificial viscosity and a predictorcorrector scheme. The construction creates an explicit scheme.We begin by considering the NSFD scheme of Mickens and that of Erdogan and Ozis for first-order equations. The latter's method formulates a method to calculate some of the denominator functions and nonlocal approximations that characterize Mickens' scheme. We extend the analysis of Erdogan and Ozis by presenting a construction for second-order nonlinear autonomous functions that naturally generates the numerator and denominator functions for Mickens' equivalent schemes. We extend this result to systems of up to three differential equations and demonstrate the simply constructed scheme's computational advantages to handle transitions between linear and nonlinear problems as well as with the inclusion or exclusion of nonhomogeneous constant terms.We include applications using the SIR model for whooping cough with a constant and nonconstant, for example, seasonally affected, transmission rate.

show abstract

Section: An Nsfd Scheme Applied To An Sir Modelmentioning

confidence: 99%

A simple construction of nonstandard finite-difference schemes for small nonlinear systems applied to SIR models

Gurski

2013

Computers & Mathematics with Applications

View full text Add to dashboard Cite

show abstract

“…, Vanden Berghe et al . and Erdogan and Ozis constructed new types of RK formulas and multi step methods, exponentially trigonometrically‐fitted methods, that are exact for some degrees of polynomials and also for some exponential and trigonometric functions. Ozawa called these methods ‘functional fitting’.…”

Section: Asymptotics Of the Second Painlevé Equationmentioning

confidence: 99%

“…The polynomial reference sets might not the best for oscillatory and decaying character of the solution of Equation (1). However, Lyche [11], Simos et al [12,13], Monovasilis et al [14], Vanden Berghe et al [15,16] and Erdogan and Ozis [17,18] constructed new types of RK formulas and multi step methods, exponentially trigonometrically-fitted methods, that are exact for some degrees of polynomials and also for some exponential and trigonometric functions. Ozawa [19] called these methods 'functional fitting' .…”

Section: Asymptotics Of the Second Painlevé Equationmentioning

confidence: 99%

Numerical study of the asymptotics of the second Painlevé equation by a functional fitting method

Erdoğan

Koçak

2013

Math Methods in App Sciences

View full text Add to dashboard Cite

The Painlevé equations arise as reductions of the soliton equations such as the Korteweg–de Vries equation, the nonlinear Schrödinger equation and so on. In this study, we are concerned with numerical approximation of the asymptotics of solutions of the second Painlevé equation on pole‐free intervals along the real axis. Classical integrators such as high order Runge–Kutta schemes might be expensive to simulate oscillation, decay and blow‐up behaviours depending on initial conditions. However, a lower order functional fitting method catches all kinds of solutions even for relatively large step sizes. Copyright © 2013 John Wiley & Sons, Ltd.

show abstract

Efficient Exponential Fitting Algorithm with Two Fitting Parameters for Oscillation Problems

Cited by 2 publications

References 1 publication

A simple construction of nonstandard finite-difference schemes for small nonlinear systems applied to SIR models

A simple construction of nonstandard finite-difference schemes for small nonlinear systems applied to SIR models

Numerical study of the asymptotics of the second Painlevé equation by a functional fitting method

Contact Info

Product

Resources

About