Exponential B-spline collocation method for solving the generalized Newell-Whitehead-Segel equation

Wasim, Imtiaz; Abbas, Muhammad; Iqbal, Muhammad Kashif; Hayat, Afzaal Mubashir

doi:10.22436/jmcs.020.04.05

Cited by 7 publications

(1 citation statement)

References 13 publications

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“…These functions are very popular because of the properties of continuity, compact support, orthogonality, and capability to handle the local phenomenon. B-spline functions of standard [27] and trigonometric forms [27] are successfully implemented to solve the well-known differential equations but the work reported in the literature using the exponential form of B-spline is less because of the involved parameter, whose value is taken as a hit and trial for reducing the errors [28,29].…”

Section: Exponential B-spline Basis Functionmentioning

confidence: 99%

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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