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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zenonas Navickas & Tadas Telksnys & Romas Marcinkevicius & Maosen Cao & Minvydas Ragulskis, 2021. "F-Operators for the Construction of Closed Form Solutions to Linear Homogenous PDEs with Variable Coefficients," Mathematics, MDPI, vol. 9(9), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:918-:d:540137
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    References listed on IDEAS

    as
    1. Ji, Bingquan & Zhang, Luming, 2020. "A dissipative finite difference Fourier pseudo-spectral method for the Klein-Gordon-Schrödinger equations with damping mechanism," Applied Mathematics and Computation, Elsevier, vol. 376(C).
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