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

Hussin, Che Haziqah Che; Mandangan, Arif; Azmi, Amirah; Kılıçman, Adem

doi:10.37934/arfmts.99.2.197206

Cited by 2 publications

(2 citation statements)

References 17 publications

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“…As expected, the results are obtained by the MMRDTM with high accuracy to the exact solutions. Hussin et al, also use the method to obtain solitary wave solutions [23][24].…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solution for Time-Fractional Nonlinear Telegraph Equations with Source Term

Abdul Rahman Farhan Sabdin,

Che Haziqah Che Hussin,

Graygorry Brayone Ekal

et al. 2023

ARASET

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In this study, we considered time-fractional nonlinear telegraph equations (TFNLTEs). For solving the TFNLTEs, we deployed a method known as the Multistep Modified Reduced Differential Transform Method (MMRDTM). Prior to the multistep technique, the nonlinear term in TFNLTEs is replaced with corresponding Adomian polynomials. It can be observed that the MMRDTM is much simpler and more straightforward. On top of that, it works exceptionally where the obtained solutions are more accurately approximated over time. To demonstrate the performance of the MMRDTM in terms of its capabilities and accuracies, we provided two numerical examples of solving TFNLTEs by using MMRDTM and Modified Reduced Differential Transform Method (MRDTM). By comparing the absolute errors of the obtained solutions by both methods, we demonstrated that the solutions provided by the MMRDTM much closer to the exact solutions compared to the corresponding solutions yielded by the MRDTM. This justified that the MMRDTM provides highly accurate and precise solutions for the TFNLTEs.

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“…As expected, the results are obtained by the MMRDTM with high accuracy to the exact solutions. Hussin et al, also use the method to obtain solitary wave solutions [23][24].…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solution for Time-Fractional Nonlinear Telegraph Equations with Source Term

Abdul Rahman Farhan Sabdin,

Che Haziqah Che Hussin,

Graygorry Brayone Ekal

et al. 2023

ARASET

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show abstract

“…From all these occurrences, the obtained results are not only produced with a minimal number of calculated terms and exceptional precision but the solutions are also obtained with high-speed convergent sequence over a broad time span. Besides that, Hussin et al, [41] also used the method to obtain solitary wave solutions.…”

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

Cited by 2 publications

References 17 publications

Approximate Analytical Solution for Time-Fractional Nonlinear Telegraph Equations with Source Term

Approximate Analytical Solution for Time-Fractional Nonlinear Telegraph Equations with Source Term

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

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