Approximate Analytic Solution of Burger Huxley Equation Using Feed-Forward Artificial Neural Network

Panghal, Shagun; Kumar, Manoj

doi:10.1007/s11063-021-10508-8

Cited by 6 publications

(2 citation statements)

References 40 publications

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“…Slavova et al [24] constructed a cellular neural network model to study the Burgers-Huxley equation. Shagun et al [25] employed a feed-forward neural network to solve the Burgers-Huxley equation and investigated the impact of the number of training points on the accuracy of the solution. Kumar et al [26] proposed a deep learning algorithm based on the deep Galerkin method for solving the Burgers-Huxley equation, which outperformed traditional numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Study of Burgers–Huxley Equation Using Neural Network Method

Wen

Chaolu

2023

Axioms

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The study of non-linear partial differential equations is a complex task requiring sophisticated methods and techniques. In this context, we propose a neural network approach based on Lie series in Lie groups of differential equations (symmetry) for solving Burgers–Huxley nonlinear partial differential equations, considering initial or boundary value terms in the loss functions. The proposed technique yields closed analytic solutions that possess excellent generalization properties. Our approach differs from existing deep neural networks in that it employs only shallow neural networks. This choice significantly reduces the parameter cost while retaining the dynamic behavior and accuracy of the solution. A thorough comparison with its exact solution was carried out to validate the practicality and effectiveness of our proposed method, using vivid graphics and detailed analysis to present the results.

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Section: Introductionmentioning

confidence: 99%

Study of Burgers–Huxley Equation Using Neural Network Method

Wen

Chaolu

2023

Axioms

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“…Shukla and Kumar [40] applied the numerical scheme based on the Crank-Nicolson finite difference method in collaboration with the Haar wavelet analysis, to obtain the numerical solution. A feed-forward artificial neural network technique is applied by Panghal and Kumar [41] in which the constructed error function is minimized using the quasi-Newton algorithm.…”

mentioning

confidence: 99%

Numerical Approximation of Generalized Burger’s-Fisher and Generalized Burger’s-Huxley Equation by Compact Finite Difference Method

Kaur

Shallu

Kumar

et al. 2021

Advances in Mathematical Physics

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In this work, computational analysis of generalized Burger’s-Fisher and generalized Burger’s-Huxley equation is carried out using the sixth-order compact finite difference method. This technique deals with the nonstandard discretization of the spatial derivatives and optimized time integration using the strong stability-preserving Runge-Kutta method. This scheme inculcates four stages and third-order accuracy in the time domain. The stability analysis is discussed using eigenvalues of the coefficient matrix. Several examples are discussed for their approximate solution, and comparisons are made to show the efficiency and accuracy of CFDM6 with the results available in the literature. It is found that the present method is easy to implement with less computational effort and is highly accurate also.

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