A Fast Implicit Integration Scheme to Solve Highly Nonlinear System

A high-order accuracy numerical method is proposed to solve the (1+1)-dimensional nonlinear Dirac equation in this work. We construct the compact finite difference scheme for the spatial discretization and obtain a nonlinear ordinary differential system. For the temporal discretization, the implicit integration factor method is applied to deal with the nonlinear system. We therefore develop two implicit integration factor numerical schemes with full discretization, one of which can achieve fourth-order accuracy in both space and time. Numerical results are given to validate the accuracy of these schemes and to study the interaction dynamics of the nonlinear Dirac solitary waves.

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Asynchronous parallel algorithm for three-dimensional soil-structure interaction analysis based on explicit-implicit integration scheme

Scientia Sinica Technologica ◽

10.1360/n092017-00212 ◽

2017 ◽

Vol 47 (12) ◽

pp. 1321-1330

Author(s):

JunQuan WANG ◽

QiFang LIU ◽

ShaoLin CHEN ◽

Hui TANG ◽

GuoLiang ZHOU

Keyword(s):

Parallel Algorithm ◽

Soil Structure ◽

Interaction Analysis ◽

Three Dimensional ◽

Soil Structure Interaction ◽

Integration Scheme ◽

Implicit Integration ◽

Structure Interaction ◽

Asynchronous Parallel

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Nonlinear System Identification in coherence with Nonlinearity measure for Dynamic Physical systems- Case Studies

10.21203/rs.3.rs-945119/v1 ◽

2021 ◽

Author(s):

Joanofarc Xavier ◽

Rames C Panda ◽

SK Patnaik

Keyword(s):

Nonlinear Dynamics ◽

System Identification ◽

Nonlinear System ◽

Case Studies ◽

Nonlinear System Identification ◽

Least Square ◽

Measurement Tool ◽

Identification Methods ◽

Physical Systems ◽

Highly Nonlinear

Abstract With the recent success of using the time series to vast applications, one would expect its boundless adaptation to problems like nonlinear control and nonlinearity quantification. Though there exist many system identification methods, finding suitable method for identifying a given process is still cryptic. Moreover, to this notch, research on their usage to nonlinear system identification and classification of nonlinearity remains limited. This article hovers around the central idea of developing a ‘kSINDYc’ (key term based Sparse Identification of Nonlinear Dynamics with control) algorithm to capture the nonlinear dynamics of typical physical systems. Furthermore, existing two reliable identification methods namely NL2SQ (Nonlinear least square method) and N3ARX (Neural network based nonlinear auto regressive exogenous input scheme) are also considered for all the physical process-case studies. The primary spotlight of present research is to encapsulate the nonlinear dynamics identified for any process with its nonlinearity level through a mathematical measurement tool. The nonlinear metric Convergence Area based Nonlinear Measure (CANM) calculates the process nonlinearity in the dynamic physical systems and classifies them under mild, medium and highly nonlinear categories. Simulation studies are carried-out on five industrial systems with divergent nonlinear dynamics. The user can make a flawless choice of specific identification methods suitable for given process by finding the nonlinear metric (Δ0). Finally, parametric sensitivity on the measurement has been studied on CSTR and Bioreactor to evaluate the efficacy of kSINDYc on system identification.

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