A New Efficient Fourth Order Collocation Scheme for Solving sine–Gordon Equation

Singh, Brajesh Kumar; Gupta, Mukesh

doi:10.1007/s40819-021-01089-0

Cited by 5 publications

(2 citation statements)

References 35 publications

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“…For numerical computation, c is taken as 0.5 with the time step as k ¼ 0:0001and space step size is h ¼ 0:02 and 0.04 compared with results as reported in the literature [16,21,36]. The number of iteration used in the PSO is 50.…”

Section: Examplementioning

confidence: 99%

“…Albowitz et al [6,7] discussed the equation for the unstable nature using the nonlinear spectrum. Various analytical and numerical approaches have been applied by the researchers to solve this equation for its soliton solutions including the modified decomposition method [8,9] for solving this equation 1D and 2D, the modified Adomian decomposition method [10] to solve the SG equation in (N + 1)-dimensions, homotopy analysis method [11], boundary element and boundary integral approach [12,13], Compact finite difference of order-6 (CFD6) scheme [14], tension spline-based approximation scheme [15], Modified cubic B-spline (MCB) collocation technique [16], localized method of approximate particular solutions [17], Legendre spectral element method [18], virtual element method [19], Barycentric rational interpolation and local radial basis functions [20], fourth-order collocation scheme [21] and rational radial basis function [22].…”

Section: Introductionmentioning

confidence: 99%

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Particle Swarm Optimization for Solving Sine-Gordan Equation

Arora¹,

Chauhan²,

Asjad³

et al. 2023

Computer Systems Science and Engineering

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The term 'optimization' refers to the process of maximizing the beneficial attributes of a mathematical function or system while minimizing the unfavorable ones. The majority of real-world situations can be modelled as an optimization problem. The complex nature of models restricts traditional optimization techniques to obtain a global optimal solution and paves the path for global optimization methods. Particle Swarm Optimization is a potential global optimization technique that has been widely used to address problems in a variety of fields. The idea of this research is to use exponential basis functions and the particle swarm optimization technique to find a numerical solution for the Sine-Gordan equation, whose numerical solutions show the soliton form and has diverse applications. The implemented optimization technique is employed to determine the involved parameter in the basis functions, which was previously approximated as a random number in the work reported till now in the literature. The obtained results are comparable with the results obtained in the literature. The work is presented in the form of figures and tables and is found encouraging.

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Section: Examplementioning

confidence: 99%