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Article

F-Operators for the Construction of Closed Form Solutions to Linear Homogenous PDEs with Variable Coefficients

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Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, 51368 Kaunas, Lithuania
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Department of Software Engineering, Kaunas University of Technology, Studentu 50-415, 51368 Kaunas, Lithuania
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College of Mechanics and Materials, Hohai University, Nanjing 210098, China
*
Author to whom correspondence should be addressed.
Academic Editor: Alberto Cabada
Mathematics 2021, 9(9), 918; https://doi.org/10.3390/math9090918
Received: 19 March 2021 / Revised: 12 April 2021 / Accepted: 18 April 2021 / Published: 21 April 2021
(This article belongs to the Section Difference and Differential Equations)
A computational framework for the construction of solutions to linear homogenous partial differential equations (PDEs) with variable coefficients is developed in this paper. The considered class of PDEs reads: ptj=0mr=0njajrtxrjpxj=0 F-operators are introduced and used to transform the original PDE into the image PDE. Factorization of the solution into rational and exponential parts enables us to construct analytic solutions without direct integrations. A number of computational examples are used to demonstrate the efficiency of the proposed scheme. View Full-Text
Keywords: Fourier transform; operator calculus; partial differential equation; linear PDE with variable coefficients Fourier transform; operator calculus; partial differential equation; linear PDE with variable coefficients
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MDPI and ACS Style

Navickas, Z.; Telksnys, T.; Marcinkevicius, R.; Cao, M.; Ragulskis, M. F-Operators for the Construction of Closed Form Solutions to Linear Homogenous PDEs with Variable Coefficients. Mathematics 2021, 9, 918. https://doi.org/10.3390/math9090918

AMA Style

Navickas Z, Telksnys T, Marcinkevicius R, Cao M, Ragulskis M. F-Operators for the Construction of Closed Form Solutions to Linear Homogenous PDEs with Variable Coefficients. Mathematics. 2021; 9(9):918. https://doi.org/10.3390/math9090918

Chicago/Turabian Style

Navickas, Zenonas, Tadas Telksnys, Romas Marcinkevicius, Maosen Cao, and Minvydas Ragulskis. 2021. "F-Operators for the Construction of Closed Form Solutions to Linear Homogenous PDEs with Variable Coefficients" Mathematics 9, no. 9: 918. https://doi.org/10.3390/math9090918

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