A new approach for the coupled advection-diffusion processes including source effects

Tahir, Shko Ali; Sarı, Murat

doi:10.1016/j.apnum.2022.10.014

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…Many mathematicians have solved such problems to date, for more details, see [1,5,8,9,13,24,25,27,35]. Few authors have studied the spline method to solve partial differential equations, for instance, in [2,21,22,30,32,36,37,40]. In this article, the cubic B-spline technique is used to solve a parabolic partial differential equation as follows:…”

Section: Introductionmentioning

confidence: 99%

Spline collocation methods for solving some types of nonlinear parabolic partial differential equations

Mahmood¹,

Tahir²,

Jwamer³

2023

J. Math. Computer Sci.

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In this work, some types of nonlinear parabolic partial differential equations have been studied by means of the collocation method with cubic B-splines, without transformation or linearization. Here, the convergence analysis of the current scheme is also theoretically investigated. A few numerical examples are given to illustrate the viability and effectiveness of the proposed technique. The error norms l 2 and l ∞ are used to assess the accuracy of the current method. In this respect, the proposed method, keeping the real features of such problems, is able to save the behavior of nonlinear terms without facing any conventional drawbacks. Furthermore, it is mathematically shown and numerically seen that there is a good agreement between the approximation and the exact solutions. The current approach reduces the cost of calculation as well as the need for storage space at various parameters.

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Section: Introductionmentioning

confidence: 99%

Spline collocation methods for solving some types of nonlinear parabolic partial differential equations

Mahmood¹,

Tahir²,

Jwamer³

2023

J. Math. Computer Sci.

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“…In the late 1970 s, Kuramoto [1] and Sivashinsky [2] independently derived the Kuramoto-Sivashinsky (KS) equation and worked on turbulence phenomena in chemistry and thermal diffusive instability in laminar flame fronts. If b = 0, then equation (1) is defined as the KS equation, which is a canonical nonlinear evolution equation with a wide range of applications in modelling various scientific engineering, and physical phenomena, including diffusion and chaos [3][4][5][6] and the flow of thin liquid membranes, reaction diffusion systems [7][8][9][10][11] and stationary solitary pulses in a falling film [12]. This equation can also be used to define long waves in a viscous fluid along an inclined plane [13,14], stress waves in fragmented porous media [15], and unstable drift waves in plasma [16].…”

Section: Introductionmentioning

confidence: 99%

An efficient scheme for solving nonlinear generalized kuramoto-sivashinksy processes

Mahmood,

Tahir,

Jwamer

2023

Phys. Scr.

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In this work, we investigate the numerical solution of generalized Kuramoto-Sivashinksy (GKS) problems based on the collocation of the quantic B-spline (QBS) and high-order strong stability-preserving Runge–Kutta (SSPRK54) scheme. When considering nonlinear parts that lose real features, we address the issue without resorting to any transformations or linearization. The efficiency and accuracy of our proposed technique are evaluated using a variety of illustrative examples. The numerical results show that our approach captured the natural behaviour of the problems well and consumed less storage space.

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A new hybrid technique based on nonpolynomial splines and finite differences for solving the Kuramoto–Sivashinsky equation

2023

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The generalized Kuramoto–Sivashinsky equation arises frequently in engineering, physics, biology, chemistry, and applied mathematics, and because of its extensive applications, this important model has received much attention regarding obtaining numerical solutions. This article introduces a new hybrid technique based on nonpolynomial splines and finite differences for solving the Kuramoto–Sivashinsky equation approximately. Specifically, the truncation error is studied to examine the convergence order of the proposed scheme, some problems are given to show its viability and effectiveness, and the norm errors are determined to compare the current method with the analytic solution and some other methods from the literature.

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A new approach for the coupled advection-diffusion processes including source effects

Cited by 3 publications

References 29 publications

Spline collocation methods for solving some types of nonlinear parabolic partial differential equations

Spline collocation methods for solving some types of nonlinear parabolic partial differential equations

An efficient scheme for solving nonlinear generalized kuramoto-sivashinksy processes

A new hybrid technique based on nonpolynomial splines and finite differences for solving the Kuramoto–Sivashinsky equation

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