Nonlinear feedback self-excitation of modal oscillations in a class of under-actuated two degrees-of-freedom mechanical systems

Kundu, Prasanjit Kumar; Chatterjee, Satyajit

doi:10.1016/j.ijnonlinmec.2021.103768

Cited by 4 publications

(1 citation statement)

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“…Some natural phenomena can be modeled by linear and non-linear systems of integral and differential equations, which are commonly used in fields such as biology, chemistry, and physics [1][2][3][4][5][6][7][8][9][10][11]. Many numerical methods, such as collocation boundary value methods, discontinuous Galerkin approximations, Euler matrix method, spectral element method, Chebyshev wavelets approach, and Radial basis Functions, have been provided to solve linear and nonlinear Volterra integral equations [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Application of the reproducing kernel method for solving linear Volterra integral equations with variable coefficients

Amoozad,

Allahviranloo,

Abbasbandy

et al. 2024

Phys. Scr.

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This article proposes a new approach for solving linear Volterra integral equations with variable coefficients using the Reproducing Kernel Method (RKM). This method eliminates the need for the Gram-Schmidt process. However, the accuracy of RKM is influenced by various factors, including the selection of points, bases, space, and implementation method. The main objective of this article is to introduce a generalized method based on the Reproducing Kernel, which is successful in solving a special type of singular weakly nonlinear boundary value problems (BVPs). The easy implementation, elimination of the Gram-Schmidt process, fewer calculations, and high accuracy of the present method are interesting. The conformity of numerical results, including tables and figures, with theorems related to error analysis and convergence order, confirms the practicality of the present method.

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