Numerical simulation of front dynamics in a nonlinear singularly perturbed reaction–diffusion problem

Argun, Raul; Volkov, V. S.; Lukyanenko, D. V.

doi:10.1016/j.cam.2022.114294

Cited by 5 publications

(3 citation statements)

References 52 publications

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“…Usually, these are algorithms from the class of implicit Runge-Kutta [168,178,179] and BDF methods [175,176,180]. The schemes of Rosenbrock type [181][182][183][184] are also suitable.…”

Section: Methods Of Lines Numerical Integration Using Mathematicamentioning

confidence: 99%

Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration

Сорокин

Vyazmin

2022

Mathematics

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The paper describes essential reaction–diffusion models with delay arising in population theory, medicine, epidemiology, biology, chemistry, control theory, and the mathematical theory of artificial neural networks. A review of publications on the exact solutions and methods for their construction is carried out. Basic numerical methods for integrating nonlinear reaction–diffusion equations with delay are considered. The focus is on the method of lines. This method is based on the approximation of spatial derivatives by the corresponding finite differences, as a result of which the original delay PDE is replaced by an approximate system of delay ODEs. The resulting system is then solved by the implicit Runge–Kutta and BDF methods, built into Mathematica. Numerical solutions are compared with the exact solutions of the test problems.

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“…Usually, these are algorithms from the class of implicit Runge-Kutta [168,178,179] and BDF methods [175,176,180]. The schemes of Rosenbrock type [181][182][183][184] are also suitable.…”

Section: Methods Of Lines Numerical Integration Using Mathematicamentioning

confidence: 99%

Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration

Сорокин

Vyazmin

2022

Mathematics

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“…When the highest spatial derivative of these partial differential equations is multiplied by a small parameter, such problems are called singularly perturbed inverse problems. Recently, a lot researchers have paid attention to develop some numerical methods for solving singularly perturbed inverse problems (see [31][32][33][34][35][36][37] and their references). It should be pointed out that the authors in [31][32][33][34][35][36][37] used the gradient method to find the solution of inverse problems for singularly perturbed partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, a lot researchers have paid attention to develop some numerical methods for solving singularly perturbed inverse problems (see [31][32][33][34][35][36][37] and their references). It should be pointed out that the authors in [31][32][33][34][35][36][37] used the gradient method to find the solution of inverse problems for singularly perturbed partial differential equations. To this day, there is no any report by using swarm intelligent optimization algorithms to solve these inverse problems.…”

Section: Introductionmentioning

confidence: 99%

An improved squirrel search algorithm for a coefficient inversion problem of a singularly perturbed reaction-diffusion equation

Mai,

Bian,

Liu

2024

Preprint

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A novel numerical algorithm is proposed for solving a coefficient inverse problem of a singularly perturbed reaction-diffusion equation with the final time observation data. Firstly, for the discretization scheme of the direct problem, the barycentric form rational spectral approach based on the sinh transformation is used to discretize the space derivative and the Crank-Nicolson finite difference scheme is utilized to approximate the time derivative. For the construction of inverse problem, we design a new fitness function about the reaction coefficient. Then integrating optimal neighborhood search strategy, random opposition based learning strategy and adaptive predator presence probability strategy, an improved squirrel search algorithm named NOISSA is proposed. Finally, 9 benchmark test functions are used to validate the performance of our proposed NOISSA. Moreover, numerical experiments are carried out to illustrate the advantage of our new algorithm in solving the coefficient inverse problems of singularly perturbed reaction-diffusion problems.

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Magnetorheological Damping Multi degree of Freedom Isolation Structure Based on Instantaneous Optimal Control Algorithm and Its Numerical Simulation

Jia¹

2022

2022 International Conference on Knowledge Engineering and Communication Systems (ICKES)

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Numerical simulation of front dynamics in a nonlinear singularly perturbed reaction–diffusion problem

Cited by 5 publications

References 52 publications

Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration

Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration

An improved squirrel search algorithm for a coefficient inversion problem of a singularly perturbed reaction-diffusion equation

Magnetorheological Damping Multi degree of Freedom Isolation Structure Based on Instantaneous Optimal Control Algorithm and Its Numerical Simulation

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