Solution of nonlinear telegraph equation with discontinuities along the transmission line using meshless collocation method
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10258150" target="_blank" >RIV/61989100:27740/25:10258150 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S2666818125001469?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2666818125001469?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.padiff.2025.101219" target="_blank" >10.1016/j.padiff.2025.101219</a>
Alternative languages
Result language
angličtina
Original language name
Solution of nonlinear telegraph equation with discontinuities along the transmission line using meshless collocation method
Original language description
In this paper, we present a novel hybrid numerical technique combining radial basis functions (RBFs) and the finite difference method (FDM) for solving the one-dimensional telegraph interface model (TIM). The presence of interfaces or discontinuities along the transmission line requires additional boundary or interface conditions to accurately describe the voltage and current behaviors at these junctions. Our method incorporates these interface conditions, approximating spatial partial derivatives using RBFs and time derivatives using FDM. To validate our approach, we applied it to several benchmark linear and nonlinear TIMs. For linear models, the resulting algebraic system is solved using Gauss elimination, while for nonlinear models, we employed the quasi-Newton method to linearize the nonlinear terms. We evaluated the method's performance by calculating the maximum absolute errors (MAEs) and root mean square errors (RMSEs) for different grid points (GPs). Additionally, we compared the true and estimate solutions through three dimensional (3D)graphs. The numerical results show that our technique provides simple implementation, quick convergence, and outstanding accuracy for both linear and nonlinear models. This hybrid approach proves to be a highly effective and reliable tool for solving telegraph interface problems. © 2025
Czech name
—
Czech description
—
Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
—
OECD FORD branch
10100 - Mathematics
Result continuities
Project
—
Continuities
O - Projekt operacniho programu
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Partial Differential Equations in Applied Mathematics
ISSN
2666-8181
e-ISSN
2666-8181
Volume of the periodical
14
Issue of the periodical within the volume
June
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
12
Pages from-to
101219
UT code for WoS article
—
EID of the result in the Scopus database
2-s2.0-105004729391