Approximate Analytical Solutions of Nonlinear Korteweg-de Vries Equations Using Multistep Modified Reduced Differential Transform Method

Hussin, Che Haziqah Che; Ismail, Ahmad Izani Md.; Kılıçman, Adem; Azmi, Amirah

doi:10.13189/ms.2020.081302

Cited by 6 publications

(5 citation statements)

References 8 publications

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“…Other researchers also used the multistep scheme by applying it on RDTM, called the multistep RDTM (MsRDTM) [29][30][31]. In 2018 and 2019, Hussin et al, [32,33] proposed and implemented the Multistep Modified RDTM (MMRDTM) in solving NLSEs and fractional NLSEs (FNLSEs) respectively. Furthermore, Che Hussin et al, [34,35] used MMRDTM then used in solving forced nonlinear Korteweg-de Vries (fNkdVE) and KdV equations with compact support.…”

Section: Introductionmentioning

confidence: 99%

Multistep Reduced Differential Transform Method in Solving Nonlinear Schrodinger Equations

Abdul Rahman Farhan Sabdin,

Che Haziqah Che Hussin,

Jumat Sulaiman

et al. 2024

ARASET

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This paper obtains semi-analytical solutions for the nonlinear Schrodinger equations (NLSEs) using the multistep reduced differential transform method (MsRDTM). The implemented method yields an analytical approximate solution over a longer time frame, in which the method applied is treated as an algorithm in a sequence of small sub-division of intervals of identical length compared to the traditional reduced differential transform method (RDTM). Excluding the need of perturbation, linearization, or discretization, this method offers the benefit and reliability of the multistep algorithm. The outcomes show that the MsRDTM generated highly accurate solutions of NLSEs than the RDTM. In addition, the results show that the suggested method is straightforward to use, saves a significant amount of computing work when solving NLSEs, and has potential for broad application in other complex partial differential equations (PDEs) in the fields of engineering and science. The accuracy of the method is shown through the tables and graphical illustrations provided.

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Section: Introductionmentioning

confidence: 99%

Multistep Reduced Differential Transform Method in Solving Nonlinear Schrodinger Equations

Abdul Rahman Farhan Sabdin,

Che Haziqah Che Hussin,

Jumat Sulaiman

et al. 2024

ARASET

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“…Apart from that, the proposed Multistep Modified Reduced Differential Transform Method (MMRDTM) has been deployed for approximating various types of well-established equations such as Non-linear Schrodinger Equations (NLSEs), Klein-Gordon equations as well as fractional NLSE [35][36][37]. Moreover, the proposed MMRDTM was also utilised for approximating the non-linear KdV equation and NLSE with power law non-linearity [38,39]. The MMRDTM has been deployed by Hussin et al, [40] for approximating NKdVEs with compactons.…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solutions for Non-linear Telegraph Equations with Source Term

Abdul Rahman Farhan Sabdin,

Che Haziqah Che Hussin,

Arif Mandangan

et al. 2023

ARASET

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This study proposed a new version of Multistep Modified Reduced Differential Transform Method (MMRDTM) which is applicable for obtaining semi-analytical approximation on Non-linear Telegraph Equations (NLTEs) with source term. Through the experimental approach, we unveiled various advantages of the proposed method, especially its ability to analytically approximate high-speed converging series. Moreover, a significant reduction in the number of calculated terms can also be observed. Before deploying the multistep technique, the substitution of non-linear term in NLTEs with the corresponding Adomian polynomial takes place. Consequently, a simpler technique for approximating NLTEs with source term was discovered. Besides that, the solutions can be estimated more precisely over a longer time. To justify our findings, solutions of NLTEs with source term are obtained using the MMRDTM. The accuracy of the proposed method for solving these equations was tested by comparing the absolute errors between the solutions obtained by the proposed method and the Modified Reduced Differential Transform Method (MRDTM) with the exact solution. The obtained solutions evidenced that the proposed MMRDTM can deliver highly precise approximations for the NLTEs with source term.

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“…Recently, nonlinear KdV equations was solved by Hussin et al, [11] using their proposed Multistep Modified Reduced Differential Transform Method (MMRDTM). Based on their finding, high-accuracy approximate solutions of the nonlinear KdV were achieved.…”

Section: Introductionmentioning

confidence: 99%

Solitary Wave Solutions for Forced Nonlinear Korteweg-de Vries Equation by Using Approximate Analytical Method

Hussin

Mandangan

Azmi

et al. 2022

ARFMTS

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The Multistep Modified Reduced Differential Transform Method (MMRDTM) is proposed in this paper. It is implemented to solve the forced nonlinear Korteweg-de Vries (fnKdV) equations. There are several advantages of the proposed method. Using the suggested approach, a high-speed converging series can be approximated analytically. Furthermore, the number of calculated terms is reduced significantly. The nonlinear term in fnKdV equations is substituted with corresponding Adomian polynomials before applying the multi-step technique. As a result, we provided simpler and more effective ways to solve fnKdV equations. On top of that, the solutions can be approximated more accurately over a longer period of time. To show the MMRDTM's capability and accuracy, we consider several of the fnKdV examples to illustrate the proposed method’s potential in analytical approximation. Then, the features of the solutions are represented in tabular and graphical forms. In conclusion, the proposed method delivers highly accurate and precise solutions for these types of equations.

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Approximate Analytical Solutions of Nonlinear Korteweg-de Vries Equations Using Multistep Modified Reduced Differential Transform Method

Cited by 6 publications

References 8 publications

Multistep Reduced Differential Transform Method in Solving Nonlinear Schrodinger Equations

Multistep Reduced Differential Transform Method in Solving Nonlinear Schrodinger Equations

Approximate Analytical Solutions for Non-linear Telegraph Equations with Source Term

Solitary Wave Solutions for Forced Nonlinear Korteweg-de Vries Equation by Using Approximate Analytical Method

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