Numerical solution of time fractional Kuramoto-Sivashinsky equation by Adomian decomposition method and applications

Kulkarni, Sharvari; Takale, Kalyanrao; Gaikwad, Shrikisan

doi:10.26637/mjm0803/0060

Cited by 2 publications

(1 citation statement)

References 12 publications

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“…In equation (1), h(x, y, t) describes the complex field and x, y, and t respectively denote spatial and temporal variables, respectively. Different techniques are investigated to find solutions for (1) [9,[25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

On short-range pulse propagation described by (2 + 1)-dimensional Schrödinger's hyperbolic equation in nonlinear optical fibers

Ali

Wazwaz

Mehanna³

et al. 2020

Phys. Scr.

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The (2 + 1)-dimensional Schrödinger complex equations are essential physical models that describe the short-range pulse spread in nonlinear media fiber optics. We construct novel complex solutions to Schrödinger’s complex hyperbolic model by using two different techniques. One method is characterized by the efficient algebraic equations that eventually form. Meanwhile, it uses the dependency variable expressions and its derivatives in the differential equation of the polynomial of a solitary wave. New acquired solutions are rational and exponential solutions expressed by periodic solutions. The solutions are illustrated through 3D- and 2D- plots to clarify the physical features for this model.

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Section: Introductionmentioning

confidence: 99%

On short-range pulse propagation described by (2 + 1)-dimensional Schrödinger's hyperbolic equation in nonlinear optical fibers

Ali

Wazwaz

Mehanna³

et al. 2020

Phys. Scr.

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show abstract

Robust Implicit Difference Approach for the Time-Fractional Kuramoto–sivashinsky Equation With the Non-Smooth Solution

et al. 2023

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This paper formulates the L1 implicit difference scheme (L1IDS) for the time-fractional Kuramoto–Sivashinsky equation (TFKSE) with non-smooth solution. The TFKSE is one of useful descriptions for modeling flame-propagation, viscous flow problems, and reaction–diffusion systems. The proposed method approximates the unknown solution by using two main stages. At the first stage, the L1 method with nonuniform meshes and the general centered difference method is adopted to discretize the Caputo fractional derivative and the spatial derivative, respectively. In the second stage, the fully-discrete L1IDS is established with the help of the Galerkin scheme based on piecewise linear test functions. Meanwhile, an iterative algorithm is adopted to solve the nonlinear systems. Furthermore, the convergence and stability of the proposed method are both demonstrated and confirmed numerically. Finally, three numerical examples highlight the accuracy and efficiency of the proposed strategy.

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Numerical solution of time fractional Kuramoto-Sivashinsky equation by Adomian decomposition method and applications

Cited by 2 publications

References 12 publications

On short-range pulse propagation described by (2 + 1)-dimensional Schrödinger's hyperbolic equation in nonlinear optical fibers

On short-range pulse propagation described by (2 + 1)-dimensional Schrödinger's hyperbolic equation in nonlinear optical fibers

Robust Implicit Difference Approach for the Time-Fractional Kuramoto–sivashinsky Equation With the Non-Smooth Solution

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