Numerical solutions of the fractional KdV-Burgers-Kuramoto equation

Kaya, Doǧan; Gülbahar, Sema; Yokuş, Asıf

doi:10.2298/tsci170613281k

Cited by 10 publications

(7 citation statements)

References 16 publications

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“…In addition, at points of discontinuity where its derivatives do not exist, the concept of integration is introduced in order to overcome the prescribed problem [20]. The Haar wavelet techniques have been used for various purposes, for example to eliminate noise from images and signals, for time-frequency analysis, to solve linear and non-linear integro differential equations (IDE), DE and IE [21][22][23][24][25][26][27][28][29]. Siraj et al investigated a multi-resolution collocation method for time-dependent inverse heat problems [30], while Aziz and Siraj developed a new method to address the two-dimensional elliptical PDEs with HW [31].…”

Section: Introductionmentioning

confidence: 99%

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An approximation of one-dimensional nonlinear Kortweg de Vries equation of order nine

2022

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This research presents the approximate solution of nonlinear Korteweg-de Vries equation of order nine by a hybrid staggered one-dimensional Haar wavelet collocation method. In literature, the underlying equation is derived by generalizing the bilinear form of the standard nonlinear KdV equation. The highest order derivative is approximated by Haar series, whereas the lower order derivatives are attained by integration formula introduced by Chen and Hsiao in 1997. The findings are shown in the form of tables and a figure, demonstrating the proposed technique’s convergence, robustness, and ease of application in a small number of collocation points.

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Section: Introductionmentioning

confidence: 99%

“…Siraj et al investigated a multi-resolution collocation method for time-dependent inverse heat problems [30], while Aziz and Siraj developed a new method to address the two-dimensional elliptical PDEs with HW [31]. Kaya et al solved the fractional equation for KdV Burgers Kuramato using HW scheme [25].…”

Section: Introductionmentioning

confidence: 99%

An approximation of one-dimensional nonlinear Kortweg de Vries equation of order nine

2022

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“…These include wavelet collocation method [25][26][27][28], wavelet Galerkin method [29], wavelet-based finite element method [30], wavelet meshless methods [31], etc. A survey of some of the earlier work can be found in [32][33][34][35][36] and a review on harmonic wavelets is presented in [37]. Applications of Haar wavelet for numerical approximations are indicated in references [38][39][40][41][42][43][44][45][46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

On the numerical solution of some differential equations with nonlocal integral boundary conditions via Haar wavelet

Aziz¹,

Nisar²,

Islam³

2022

PEAS

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Differential equations with nonlocal boundary conditions are used to model a number of physical phenomena encountered in situations where data on the boundary cannot be measured directly. This study explores numerical solutions to elliptic, parabolic and hyperbolic equations with two different types of nonlocal integral boundary conditions. The numerical solutions are obtained using the Haar wavelet collocation method with the aid of Finite Differences for time derivatives. The method is applicable to both linear and nonlinear problems. To obtain the numerical solutions, Gauss elimination method is used for linear and Newton's method for nonlinear differential equations. The validity of the proposed method is demonstrated by solving several benchmark test problems from the literature: two elliptic linear and two nonlinear samples covering both types of nonlocal integral boundary conditions; one nonlinear and two linear test problems for parabolic partial differential equations; two linear samples for hyperbolic partial differential equations. The accuracy of the method is verified by comparing the numerical results with the analytical solutions. The numerical results confirm that the method is simple and effective.

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“…Others, like Koonin and Cetron, asserted that case isolation, household quarantine, and internal travel restrictions are also necessary for virus control [ 19 ]. Therefore, many mathematical properties of real world problems including fractional or integer order have been introduced to better understanding of deeper properties and to analyze by many researchers [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 ].…”

Section: Introductionmentioning

confidence: 99%

Novel Dynamic Structures of 2019-nCoV with Nonlocal Operator via Powerful Computational Technique

Gao

Veeresha

Prakasha

et al. 2020

Biology

135

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In this study, we investigate the infection system of the novel coronavirus (2019-nCoV) with a nonlocal operator defined in the Caputo sense. With the help of the fractional natural decomposition method (FNDM), which is based on the Adomian decomposition and natural transform methods, numerical results were obtained to better understand the dynamical structures of the physical behavior of 2019-nCoV. Such behaviors observe the general properties of the mathematical model of 2019-nCoV. This mathematical model is composed of data reported from the city of Wuhan, China.

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Numerical solutions of the fractional KdV-Burgers-Kuramoto equation

Cited by 10 publications

References 16 publications

An approximation of one-dimensional nonlinear Kortweg de Vries equation of order nine

An approximation of one-dimensional nonlinear Kortweg de Vries equation of order nine

On the numerical solution of some differential equations with nonlocal integral boundary conditions via Haar wavelet

Novel Dynamic Structures of 2019-nCoV with Nonlocal Operator via Powerful Computational Technique

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