Mixed Anti-Newtonian-Gaussian Rule for Real Definite Integrals

Jena, Saumya Ranjan; Nayak, D.; Paul, Abhijit; Mishra, Shubham

doi:10.37418/amsj.9.11.115

Cited by 3 publications

(3 citation statements)

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“…It also occurs in related to long waves on the interface between fluids (Hooper & Grimshaw, 1985), flame front instability (Sivashinsky, 1983), unstable drift wave in plasmas and reactiondiffusion systems (Kuramoto & Tsuzuki, 1976), model solitary pulses in a falling thin film (Saprykin, Demekhin, & Kalliadasis, 2005) and oscillating chemical reaction in a homogeneous medium (Conte, 2003). The numerical integration suggested by Dash and Jena (2008, Jena and Dash (2009, 2015a, 2015b, Jena, Nayak, and Acharya (2017), Nayak, Jena, and Acharya (2017), Jena and Singh (2015, , Jena & Nayak, 2015, 2020, Jena, Nayak, Paul, & Mishra, 2020, Jena and Mishra (2015, Jena (2018), Jena, Meher, andPaul (2016), Meher, Jena, and Paul (2017), Mohanty, Hota, and Jena (2014).…”

Section: Introductionmentioning

confidence: 99%

Numerical treatment of Kuramoto-Sivashinsky equation on B-spline collocation

Jena

Gebremedhin

2021

Arab Journal of Basic and Applied Sciences

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In this article, a nonic B-spline collocation approach is applied to solve the approximate solution of Kuramoto-Sivashinsky equation (KSE). Here the nonlinear term of KSE is linearizing using Taylor series technique. The main objective of this study is to provide a new class of approach by applying some possible higher-order derivatives rather than lower order derivatives of the nonic B-spline on the boundary conditions of KSE in finding the additional constraints, which help us to obtain a unique solution of the problem. The stability analysis is investigated using the Von-Neumann scheme and the proposed scheme is found to be unconditionally stable. The efficiency and accuracy of the proposed approach are demonstrated by two numerical tests and the current results are compared with the exact solution and result of others in the literature.

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Section: Introductionmentioning

confidence: 99%

Numerical treatment of Kuramoto-Sivashinsky equation on B-spline collocation

Jena

Gebremedhin

2021

Arab Journal of Basic and Applied Sciences

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“…In general, several attempts have been made to solve nonlinear differential equations using different methods such as mixed quadrature rules, mixed anti-Newtonian–Gaussian rules, and hybrid block approach (e.g., Dash and Jena, 2015; Gebremedhin and Jena, 2019; Jena and Dash, 2015a, 2015b; Jena and Singh, 2015; Jena and Mishra, 2015; Jena et al, 2016; Jena et al, 2017; Jena and Mohanty,2021; Jena et al, 2020a, 2020b, 2020c; Jena and Nayak, 2020; Jena and Gebremedhin, 2020; Jena and Gebremedhin, 2021; Mohanty et al, 2021). However, these methods are generally very time consuming and therefore may not be suitable for practical applications.…”

Section: Introductionmentioning

confidence: 99%

“…However, these methods are generally very time consuming and therefore may not be suitable for practical applications. To provide more efficient methods, the linearization of nonlinear equations has been recently proposed by several researchers (e.g., Gebremedhin and Jena 2020; Jena et al, 2018; Jena et al, 2020a, 2020b, 2020c; Mohanty and Jena, 2018). In this method, the nonlinear viscous dampers are linearized to simplify the design process in accordance with seismic design guidelines (e.g., response spectrum analysis method).…”

Section: Introductionmentioning

confidence: 99%

A new modified stochastic linearization technique to analyze structures with nonlinear fluid viscous dampers

Asadpour

Asadi

Hajirasouliha

2021

Journal of Vibration and Control

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Nonlinear viscous dampers can efficiently improve the seismic performance of structures by dissipating large amounts of earthquake-induced energy. In common practice, the spectral analysis of structures with nonlinear viscous dampers is generally conducted based on an estimated equivalent damping ratio. To this end, the stochastic linearization technique can be used as an effective probabilistic approach to take into account the evolutionary characteristics of the input earthquake excitation. This study aims to present optimal non-Gaussian probability density functions to improve the accuracy of the stochastic linearization technique for nonlinear viscous dampers in both firm and soft soil-based structures. It is shown that by using the optimum probability density functions, the computational error of the stochastic linearization technique for a single-degree-of-freedom structure under simulated ground motions, with a range of peak ground accelerations between 0.1 and 0.6 g, is reduced by up to 70%. The efficiency of the proposed probability density functions is then demonstrated for multi-degree-of-freedom structures, by estimating the roof displacements of a six-story steel frame with nonlinear viscous dampers under a set of natural ground motions using different linearization methods. The comparison of the stochastic linearization technique estimated responses with the exact values confirms that using the proposed probability density functions leads to considerably lower errors in both firm and soft soil-based structures compared with the other linearization techniques.

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