Numerical solutions of the Benjamin–Bona–Mahony equation using the differential quadrature method with shifted legendre and generalized Laguerre polynomials

Indian Journal of Pure and Applied Mathematics, Journal Year: 2025, Volume and Issue: unknown

Published: Jan. 18, 2025

Language: Английский

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Solution of imprecisely defined nonlinear time-fractional Fisher equation using fractional reduced differential transform method

Engineering Computations, Journal Year: 2025, Volume and Issue: 42(4), P. 1554 - 1576

Published: April 28, 2025

Purpose The study aims to obtain a semi-analytical solution for the fuzzy time-fractional Fisher equation (FtfFE) considering uncertain coefficients involved in initial condition as triangular number (TFN). Design/methodology/approach Fractional reduced differential transform method (FRDTM) has been used find convergent series both crisp and environment. Findings found using FRDTM obtained is compared with exact integer case α = 1. lower upper bound solutions of FtfFE different spatial temporal values at 0.75 are provided. relation between bounds fractional order evaluated. Originality/value Application behavior other characteristics solution.

Language: Английский

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Time-fractional shallow water wave equation with fuzzy uncertainty

Physics of Fluids, Journal Year: 2025, Volume and Issue: 37(5)

Published: May 1, 2025

This work aims to derive approximate analytical solutions for the Simplified Modified Camassa–Holm (SMCH) equation incorporating time-fractional derivatives in Caputo sense. is relevant modeling shallow water wave propagation, with significant application mathematical physics and engineering sciences. While classical formulations assume crisp variables parameters, real-world scenarios often involve inherent imprecision uncertainty. To address this, fuzzy uncertainty incorporated into formulation by introducing parameters initial conditions. A key novelty of this lies fractional reduced differential transform method obtain both precise SMCH equation. Unlike existing methods, our approach effectively handles fractional-order dynamics under assess reliability discussed method, a comparative analysis conducted between special case solutions. The obtained are presented forms, comprehensive two- three-dimensional graphical representations enhance interpretation their physical significance across various parameter values. Additionally, tabular results provided offer clearer understanding convergence behavior solution.

Language: Английский

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A fuzzy semi-analytical approach for modeling uncertainties in solitary wave solution of coupled nonlinear Boussinesq equations

Physica Scripta, Journal Year: 2024, Volume and Issue: 99(10), P. 105218 - 105218

Published: Aug. 22, 2024

Abstract This article presents the precise solitary wave solution (SWS) of nonlinear coupled Boussinesq equations (BEs) in shallow water using Homotopy Perturbation Transform Method (HPTM) and Fuzzy HPTM (FHPTM). The study introduces a fuzzy model for BEs by incorporating uncertainties depth coefficients. effectiveness FHPTM is demonstrated through comparison with exact crisp case, double parametric approach to highlight fuzziness solution. Numerical results under various scenarios are examined understand behavior SWS. compared those derived from Adomian Decomposition (ADM). show good agreement both numerical techniques.

Language: Английский

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Fuzzy uncertainty modeling of generalized Hirota–Satsuma coupled Korteweg–de Vries equation

Physics of Fluids, Journal Year: 2024, Volume and Issue: 36(9)

Published: Sept. 1, 2024

This article explores the solitary wave solutions of a generalized Hirota–Satsuma Coupled Korteweg–de Vries (HSCKdV) equation. The HSCKdV equation is mathematical model that describes certain types long waves, particularly those found in shallow water. solved exactly using Homotopy Perturbation Transform Method (HPTM). By applying this technique, authors obtain form convergent power series. These offer an understanding characteristics waves within domain water waves. has been adomian decomposition method, and results have compared with obtained from HPTM. comparison demonstrates effectiveness HPTM solving such nonlinear equations. Further, extended to fuzzy version considering initial condition as parameter. Uncertainty addressed by representing it triangular trapezoidal numbers. subsequently tackled (FHPTM) providing bound solutions. Using FHPTM, we explain results, highlighting how splits into two noting lower upper are interchanged due negative results.

Language: Английский

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Double parametric based solution of fuzzy unconfined aquifer problem using Laplace transforms method

Physics of Fluids, Journal Year: 2024, Volume and Issue: 36(11)

Published: Nov. 1, 2024

The Boussinesq equation describes the model for horizontal water flow in unconfined aquifers without precipitation, a topic that has been extensively studied literature. However, parameters, as well initial and boundary conditions, are often assumed to be exact. In reality, these conditions may incomplete or uncertain due limited knowledge, insufficient information, errors introduced by humans machines. fuzzy set theory recently successfully employed such uncertainties. This article investigates analytical solution of one-dimensional environment. objective this research is investigate recharge discharge semi-infinite aquifer adjacent lake. For present investigation, uncertainties terms considered only involved problem, whereas other parameters crisp analysis double parametric form number alongside Laplace transform techniques. obtained solutions were then compared with existing results specific cases validate their accuracy.

Language: Английский

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