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    A novel method for nonlinear singular oscillators
    (Sage Publications Ltd, 2021) Akgul, Ali; Ahmad, Hijaz; Chu, Yu-Ming; Thounthong, Phatiphat
    The present work deals with a study of a nonlinear singular oscillator. To approximate the frequency-amplitude relationship of the singular oscillator, reproducing kernel method is employed. The approximate solution is compared with the exact solution as well as the results obtained by the He's frequency-amplitude formulation, to show the effectiveness of the proposed technique for solving the problem.
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    Numerical solution of time-fractional coupled Korteweg-de Vries and Klein-Gordon equations by local meshless method
    (Indian Acad Sciences, 2021) Khan, Muhammad Nawaz; Ahmad, Imtiaz; Akgul, Ali; Ahmad, Hijaz; Thounthong, Phatiphat
    This article provides numerical simulations of the time-fractional coupled Korteweg-de Vries and Klein-Gordon equations via the local meshless collocation method (LMCM) utilising the radial basis functions. The recommended local meshless technique is utilised for the space derivatives of the models whereas Caputo fractional definition is used for time-fractional derivative. Numerical experiments are performed for one-dimensional coupled Korteweg-de Vries and two-dimensional Klein-Gordon equations. In order to verify the efficiency and accuracy of the proposed meshless method, numerical results are compared with exact and numerical techniques reported in recent literature which reveals that the method is computationally attractive and produces better results.