The Burgers Equation for a New Continuum Model with Consideration of Driver’s Forecast Effect

Yu, Lei; Zhou, Bingchang

doi:10.1155/2014/539459

Cited by 2 publications

(1 citation statement)

References 28 publications

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“…In this section, three test systems are considered as high-order bilinear systems that should be approximated by the proposed method. The first test system is the Burgers' equation which is widely used in numerous fields of applied mathematics, such as fluid mechanics [37], heat transfer [38], and traffic flow problems [39]. The second test system is a nonlinear transmission line circuit.…”

Section: Simulation Resultsmentioning

confidence: 99%

Reduced-Order Approximation of Bilinear Systems Using a New Hybrid Method based on Balanced Truncation and Iterative Rational Krylov Algorithms

Nasiri Soloklo,

Bigdeli

2023

Scientia Iranica

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In this work, a hybrid approach is proposed for the reduced order approximation of the bilinear system by combining the Balanced Truncation (BT) and Bilinear Iterative Rational Krylov Algorithm (BIRKA). Bilinear BT (BBT) has low accuracy but guarantees stability, while BIRKA convergence suffers from sensitivity to initial choice of reduced-order system. To start, the proposed approach minimizes the Integral Square Error (ISE) index to specify the order of the reduced bilinear approximation. To assurance BIRKA convergence, two approaches, BBT and Linear BT (LBT), are applied to prepare the initial guess of the reduced-order approximation.Although BBT prepare a good stable initial guess for BIRKA, solving the generalized Lyapunov equations to find the solution is very computationally expensive. The initial guess is provided by LBT through solving the Lyapunov equations, which decreases computational complexity. Furthermore, the eigenvalues are replaced by the condition number in BIRKA to decrease complexity. To verify the efficiency of the proposed approach, three bilinear test systems are being examined. Finally, the performance of the proposed approach is compared with several classical approaches. The finding 2 indicate that the convergence probability of BIRKA increases. Also, the time for the determining the Model Order Reduction (MOR) decreases.

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Section: Simulation Resultsmentioning

confidence: 99%

Reduced-Order Approximation of Bilinear Systems Using a New Hybrid Method based on Balanced Truncation and Iterative Rational Krylov Algorithms

Nasiri Soloklo,

Bigdeli

2023

Scientia Iranica

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Numerical Method for Non-Linear Conservation Laws: Inviscid Burgers Equation

Hemel¹,

Azam²,

Alam³

2021

JAMP

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This paper deals with the Burgers equation which is the most common model used in the nonlinear conservation laws. Here the theoretical aspect of conservation law is discussed by using inviscid Burgers equation. At first, we introduce the general non-linear conservation law as a partial differential equation and its solution procedure by the method of characteristic. Next, we present the weak solution of the problem with entropy condition. Taking into account shock wave and rarefaction wave, the Riemann problem has also been discussed. Finally, the finite volume method is considered to approximate the numerical solution of the inviscid Burgers equation with continuous and discontinuous initial data. An illustration of the problem is provided by some examples. Moreover, the Godunov method provides a good approximation for the problem.

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The Burgers Equation for a New Continuum Model with Consideration of Driver’s Forecast Effect

Cited by 2 publications

References 28 publications

Reduced-Order Approximation of Bilinear Systems Using a New Hybrid Method based on Balanced Truncation and Iterative Rational Krylov Algorithms

Reduced-Order Approximation of Bilinear Systems Using a New Hybrid Method based on Balanced Truncation and Iterative Rational Krylov Algorithms

Numerical Method for Non-Linear Conservation Laws: Inviscid Burgers Equation

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