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

Zenonas Navickas, Tadas Telksnys, Romas Marcinkevicius, Maosen Cao and Minvydas Ragulskis
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Zenonas Navickas: Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, 51368 Kaunas, Lithuania
Tadas Telksnys: Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, 51368 Kaunas, Lithuania
Romas Marcinkevicius: Department of Software Engineering, Kaunas University of Technology, Studentu 50-415, 51368 Kaunas, Lithuania
Maosen Cao: College of Mechanics and Materials, Hohai University, Nanjing 210098, China
Minvydas Ragulskis: Center for Nonlinear Systems, Kaunas University of Technology, Studentu 50-147, 51368 Kaunas, Lithuania

Mathematics, 2021, vol. 9, issue 9, 1-13

Abstract: 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: ? p ? t ? ? j = 0 m ? r = 0 n j a j r t x r ? j p ? x j = 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.

Keywords: Fourier transform; operator calculus; partial differential equation; linear PDE with variable coefficients (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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