Periodic boundary-value problem for a fourth-order differential equation

Abstract. Currently, one of the biggest challenges facing the state HEI is the problem for commercialization of intellectual activity results using technology transfer funds into the real economy. However, if the creating products processes ends in Research and Development stage, everything is quite transparent and clear here, but at the stage of transition to the process of self-production and sales there appears a number of difficult problems solvable. To simplify the interaction between the university and the enterprises of the real economy are invited to create an engineering center as a separate entity, affiliated with the university, whose tasks will include the issues of technology transfer to the real economy, as well as the establishment of an external production site, to address the commercialization of tasks results of intellectual activity without involving in this process the intermediate third-party organizations.

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Engineering Center as a tool for HEI’s scientific and innovation potential integration in the real economy

Minkin

Izotov

Ananova

2017

SHS Web Conf.

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An efficient Fourier spectral method and error analysis for the fourth order problem with periodic boundary conditions and variable coefficients

Jiang¹,

2023

MATH

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<abstract><p>We propose in this paper an efficient algorithm based on the Fourier spectral-Galerkin approximation for the fourth-order elliptic equation with periodic boundary conditions and variable coefficients. First, by using the Lax-Milgram theorem, we prove the existence and uniqueness of weak solution and its approximate solution. Then we define a high-dimensional $ L^2 $ projection operator and prove its approximation properties. Combined with Céa lemma, we further prove the error estimate of the approximate solution. In addition, from the Fourier basis function expansion and the properties of the tensor, we establish the equivalent matrix form based on tensor product for the discrete scheme. Finally, some numerical experiments are carried out to demonstrate the efficiency of the algorithm and correctness of the theoretical analysis.</p></abstract>

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Periodic boundary-value problem for a fourth-order differential equation

Cited by 2 publications

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Engineering Center as a tool for HEI’s scientific and innovation potential integration in the real economy

Engineering Center as a tool for HEI’s scientific and innovation potential integration in the real economy

An efficient Fourier spectral method and error analysis for the fourth order problem with periodic boundary conditions and variable coefficients

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