A comparison study of two modified analytical approach for the solution of nonlinear fractional shallow water equations in fluid flow

Sunil Kumar; Amit Kumar; Zaid Odibat; Mujahed Aldhaifallah; Kottakkaran Sooppy Nisar; Sunil Kumar; Amit Kumar; Zaid Odibat; Mujahed Aldhaifallah; Kottakkaran Sooppy Nisar

doi:10.3934/math.2020197

AIMS Mathematics

2020, Volume 5, Issue 4: 3035-3055. doi: 10.3934/math.2020197

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A comparison study of two modified analytical approach for the solution of nonlinear fractional shallow water equations in fluid flow

1.
Department of Mathematics, National Institute of Technology, Jamshedpur, 831014, Jharkhand, India
2.
Department of Mathematics, Balarampur College Purulia- 723143, West Bengal, India
3.
Department of Mathematics, Faculty of science, Al-Balqa Applied University, Salt 19117, Jordan
4.
Systems Engineering Department, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Saudi Arabia
5.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia

Received: 29 October 2019 Accepted: 16 March 2020 Published: 20 March 2020
MSC : 26A33, 34A08, 46M22

Abstract
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In this study, a comparison between the modified homotopy analysis transform method (MHATM) and residual power series method (RPSM) have been given for solving time-fractional coupled shallow water equations (SWEs). The time-fractional coupled SWEs are a system of PDEs that describe the flow below a pressure surface in a fluid is considered. Rigorous convergence analysis and error estimated have been exhibited for both the featured methods. The results obtained by MHATM and RPSM are then compared with well-known exact solutions. To show the effectiveness and advantage of the featured techniques the numerical simulation of coupled SWEs has been represented graphically with tabulated data. However, the results indicate that MHATM provides more accurate value than RPSM for solving fractional coupled SWEs.
- fractional shallow water equation,
- fractional power series,
- RPSM,
- HATM,
- homotopy polynomials,
- optimal value
Citation: Sunil Kumar, Amit Kumar , Zaid Odibat, Mujahed Aldhaifallah, Kottakkaran Sooppy Nisar. A comparison study of two modified analytical approach for the solution of nonlinear fractional shallow water equations in fluid flow[J]. AIMS Mathematics, 2020, 5(4): 3035-3055. doi: 10.3934/math.2020197

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Abstract

In this study, a comparison between the modified homotopy analysis transform method (MHATM) and residual power series method (RPSM) have been given for solving time-fractional coupled shallow water equations (SWEs). The time-fractional coupled SWEs are a system of PDEs that describe the flow below a pressure surface in a fluid is considered. Rigorous convergence analysis and error estimated have been exhibited for both the featured methods. The results obtained by MHATM and RPSM are then compared with well-known exact solutions. To show the effectiveness and advantage of the featured techniques the numerical simulation of coupled SWEs has been represented graphically with tabulated data. However, the results indicate that MHATM provides more accurate value than RPSM for solving fractional coupled SWEs.

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