Analysis of nonlinear systems arise in thermoelasticity using fractional natural decomposition scheme

2021 ◽  
Author(s):  
Deepak Umrao Sarwe ◽  
Vinayak S. Kulkarni
Keyword(s):  
Nonlinear Systems ◽  
Decomposition Scheme ◽  
Natural Decomposition

An efficient technique for two-dimensional fractional order biological population model

2020 ◽  
Vol 11 (01) ◽  
pp. 2050005 ◽  
Author(s):  
P. Veeresha ◽  
D. G. Prakasha
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Fractional Order ◽  
Population Model ◽  
Decomposition Method ◽  
Arbitrary Order ◽  
Two Dimensional ◽  
Decomposition Scheme ◽  
Biological Population ◽  
Natural Decomposition

In this paper, we find the solutions for two-dimensional biological population model having fractional order using fractional natural decomposition method (FNDM). The proposed method is a graceful blend of decomposition scheme with natural transform, and three examples are considered to validate and illustrate its efficiency. The nature of FNDM solution has been captured for distinct arbitrary order. In order to illustrate the proficiency and reliability of the considered scheme, the numerical simulation has been presented. The obtained results illuminate that the considered method is easy to apply and more effective to examine the nature of multi-dimensional differential equations of fractional order arisen in connected areas of science and technology.

The Reduced Space Shooting Method for Calculating the Peak Periodic Solutions of Nonlinear Systems

2018 ◽  
Vol 13 (6) ◽  
Author(s):  
Haitao Liao ◽  
Wenwang Wu
Keyword(s):  
Nonlinear Systems ◽  
Optimization Problem ◽  
Shooting Method ◽  
Hybrid Approach ◽  
Equality Constraints ◽  
Bound Constraints ◽  
Sqp Method ◽  
Decomposition Scheme ◽  
Reduced Space ◽  
Nonlinear Equality

A hybrid approach which combines the reduced sequential quadratic programing (SQP) method with the shooting method is proposed to search the worst resonance response of nonlinear systems. The shooting method is first employed to construct the nonlinear equality constraints for the constrained optimization problem. Then, the complex optimization problem is simplified and solved numerically by the reduced SQP method. By virtue of the coordinate basis decomposition scheme which exploits the gradients of nonlinear equality constraints, the nonlinear equality constraints are eliminated, resulting in a simple optimization problem subject to bound constraints. Moreover, the second-order correction (SOC) technique is adopted to overcome Maratos effect. The novelty of the approach described lies in the capability to efficiently handle nonlinear equality constraints. The effectiveness of the proposed algorithm is demonstrated by two benchmark examples seen in the literature.

Identification of Continuous-time Nonlinear Systems via Local Gaussian Process Models

2014 ◽  
Vol 134 (11) ◽  
pp. 1708-1715
Author(s):  
Tomohiro Hachino ◽  
Kazuhiro Matsushita ◽  
Hitoshi Takata ◽  
Seiji Fukushima ◽  
Yasutaka Igarashi
Keyword(s):  
Nonlinear Systems ◽  
Gaussian Process ◽  
Continuous Time ◽  
Process Models ◽  
Gaussian Process Models

Modeling of Nonlinear Systems using Genetic Algorithm

2012 ◽  
Vol 132 (6) ◽  
pp. 913-918 ◽  
Author(s):  
Kayoko Hayashi ◽  
Toru Yamamoto ◽  
Kazuo Kawada
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Systems
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