Numerical solution to the Gray-Scott Reaction-Diffusion equation using Hyperbolic B-spline

Kaur, Navneet; Joshi, Varun

doi:10.1088/1742-6596/2267/1/012072

Cited by 4 publications

(2 citation statements)

References 23 publications

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“…The simulation of the coupled model has been carried out by Owolabi et al [30] using the higher-order Runge-Kutta method. The well-known Gray-Scott model's numerical findings have been calculated using the help of the hyperbolic B-spline [31]. In order to analyze the ionic version of the model while it is being affected by an electric field, the Galerkin method has been deployed [32].…”

Section: Introductionmentioning

confidence: 99%

Galerkin-Bernstein Approximations of the System of Time Dependent Nonlinear Parabolic PDEs

Ali,

Trisha,

Islam

2023

GLM

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The purpose of the research is to find the numerical solutions to the system of time dependent nonlinear parabolic partial differential equations (PDEs) utilizing the Modified Galerkin Weighted Residual Method (MGWRM) with the help of modified Bernstein polynomials. An approximate solution of the system has been assumed in accordance with the modified Bernstein polynomials. Thereafter, the modified Galerkin method has been applied to the system of nonlinear parabolic PDEs and has transformed the model into a time dependent ordinary differential equations system. Then the system has been converted into the recurrence equations by employing backward difference approximation. However, the iterative calculation is performed by using the Picard Iterative method. A few renowned problems are then solved to test the applicability and efficiency of our proposed scheme. The numerical solutions at different time levels are then displayed numerically in tabular form and graphically by figures. The comparative study is presented along with L2 norm, and L∞ norm.

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Section: Introductionmentioning

confidence: 99%

Galerkin-Bernstein Approximations of the System of Time Dependent Nonlinear Parabolic PDEs

Ali,

Trisha,

Islam

2023

GLM

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“…[20] and trigonometric cubic B-spline algorithm was studied by Onarcan et all [21]. Specific RDS models were studied with finite element methods by the researchers [22,23]. Very recently Hepson O.E.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of Reaction-Diffusion Equation Systems With Trigonometric Quintic B-Spline Collocation Algorithm

Onarcan

Adar

Dağ

2023

Eskişehir Technical University Journal of Science and Technology a - Applied Sciences and Engineering

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In this study, trigonometric quintic B-spline collocation method is constructed for computing numerical solutions of the reaction-diffusion system (RDS). Schnakenberg, Gray-Scott and Brusselator models are special cases of reaction-diffusion systems considered as examples in this paper. Crank-Nicolson formulae is used for the time discretization of the generalized RDS and the nonlinear terms in time-discretized form of RDS are linearized using the Taylor expansion. The fully integration of the generalized system is carried out using the collocation method based on the trigonometric quintic B-splines. The method is tested on different problems to illustrate the accuracy. The error norms are calculated for the linear problem whereas the relative error is given for nonlinear problems. Both simple and easy B-spline algorithms are illustrated to give the solutions of RDS and also the graphical representation of the efficient solutions are presented for the nonlinear RDSs. Combination of the quintic B-splines and the collocation method is shown to present numerical solutions of the RDS successfully. With the presented method, it is possible to get approximate solutions as well as their derivatives up to an order of four on the problem domain.

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Numerical simulation of the time fractional Gray-Scott model on 2D space domains using radial basis functions

Sakariya,

Kumar

2024

J Math Chem

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Numerical solution to the Gray-Scott Reaction-Diffusion equation using Hyperbolic B-spline

Cited by 4 publications

References 23 publications

Galerkin-Bernstein Approximations of the System of Time Dependent Nonlinear Parabolic PDEs

Galerkin-Bernstein Approximations of the System of Time Dependent Nonlinear Parabolic PDEs

Numerical Solutions of Reaction-Diffusion Equation Systems With Trigonometric Quintic B-Spline Collocation Algorithm

Numerical simulation of the time fractional Gray-Scott model on 2D space domains using radial basis functions

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