| Title |
F-operators for the construction of closed form solutions to linear homogenous PDEs with variable coefficients / |
| Authors |
Navickas, Zenonas ; Telksnys, Tadas ; Marcinkevicius, Romas ; Cao, Maosen ; Ragulskis, Minvydas |
| DOI |
10.3390/math9090918 |
| Full Text |
|
| Is Part of |
Mathematics.. Basel : MDPI. 2021, vol. 9, iss. 9, art. no. 918, p. 1-13.. ISSN 2227-7390 |
| Keywords [eng] |
Fourier transform ; operator calculus ; partial differential equation ; linear PDE with variable coefficients |
| Abstract [eng] |
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−∑mj=0(∑njr=0ajr(t)xr)∂jp∂xj=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. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2021 |
| CC license |
|
