An implicit nonlinear difference scheme for two-dimensional time-fractional Burgers’ equation with time delay

Xiao, Mingcong; Wang, Zhen; Mo, Yan

doi:10.1007/s12190-023-01863-x

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…where 0 < λ ∆ < 1; for ∆ = 1, 2, 3, ..., l. This is one of the well-known delay differential equations (DDEs) that arise in a variety of real-life applications, including electronic systems [22], dynamical systems, population dynamics [23], quantum mechanics, traffic models, biological systems [24], navigational control of aircraft, economy, etc, also see in [25][26][27][28]. The DDEs are a specific kind of differential equation that considers not only the current state of a system but also its past states.…”

Section: Introductionmentioning

confidence: 99%

Fractional order Jacobi wavelet-based numerical analysis of fractal-fractional multi-pantograph delay differential equation with variable coefficients

Singh,

Verma

2024

Preprint

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In this study, the fractal-fractional Caputo and Caputo-Fabrizio derivatives are used to formulate the fractal-fractional model of multi-pantograph delay differential equations with variable coefficients. The wavelet method is constructed to provide a numerical solution by using fractional-order Jacobi wavelets. This methodology relies on the operational matrix for fractal-fractional integration of fractional order Jacobi wavelets and the collocation method. We defined pseudo code and stability analysis of the proposed approach for the given model. The error analysis and comparison of the numerical results are also shown in the tables and graphs for the three illustrative examples. In the proposed methods, the data are obtained on different values of fractal \((\nu)\) and fractional \((\mu,\phi)\) parameters and it is noteworthy to point out that the classical case is recovered for \(\mu=1\) and \(\nu=1\).

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Section: Introductionmentioning

confidence: 99%

Fractional order Jacobi wavelet-based numerical analysis of fractal-fractional multi-pantograph delay differential equation with variable coefficients

Singh,

Verma

2024

Preprint

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“…Periodic-wave solutions to 2D-BLMPE were constructed via the Riemann theta function [31]. Some other relevant works were carried out, also [32][33][34][35][36][37]. In the present work, approximate similarity solutions of some functional BLMPEs with constant coefficients are derived.…”

Section: Introductionmentioning

confidence: 99%

Insight into Functional Boiti–Leon–Mana–Pempinelli Equation and Error Control: Approximate Similarity Solutions

Alqhtani,

Srivastava,

Abdel-Gawad

et al. 2023

Mathematics

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The Boiti–Leon–Mana–Pempinelli Equation (BLMPE) is an essential mathematical model describing wave propagation in incompressible fluid dynamics. In the present manuscript, a novel generalization of the BLMPE is introduced, called herein the functional BLMPE (F-BLMPE), which involves different functions, including exponential, logarithmic and monomaniacal functions. In these cases, the F-BLMPE reduces to an explicit form in the dependent variable. In addition to this, it is worth deriving approximate similarity solutions of the F-BLMPE with constant coefficients using the extended unified method (EUM). In this method, nonlinear partial differential equation (NLPDE) solutions are expressed in polynomial and rational forms through an auxiliary function (AF) with adequate auxiliary equations. Exact solutions are estimated using formal solutions substituted into the NLPDEs, and the coefficients of the AF of all powers are set equal to zero. This approach is valid when the NLPDE is integrable. However, this technique is not valid for non-integrable equations, and only approximate solutions can be found. The maximum error can be controlled by an adequate choice of the parameters in the residue terms (RTs). Multiple similarity solutions are derived, and the ME is depicted in various examples within this work. The results found here confirm that the EUM is an efficient method for solving NLPDEs of the F-BLMPE type.

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A new nonlinear compact difference scheme for a fourth-order nonlinear Burgers type equation with a weakly singular kernel

Li,

Zhang,

Yang

2024

J. Appl. Math. Comput.

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An implicit nonlinear difference scheme for two-dimensional time-fractional Burgers’ equation with time delay

Cited by 4 publications

References 25 publications

Fractional order Jacobi wavelet-based numerical analysis of fractal-fractional multi-pantograph delay differential equation with variable coefficients

Fractional order Jacobi wavelet-based numerical analysis of fractal-fractional multi-pantograph delay differential equation with variable coefficients

Insight into Functional Boiti–Leon–Mana–Pempinelli Equation and Error Control: Approximate Similarity Solutions

A new nonlinear compact difference scheme for a fourth-order nonlinear Burgers type equation with a weakly singular kernel

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