On the Numerical Simulation of HPDEs Using ? -Weighted Scheme and the Galerkin Method

Haifa Bin Jebreen and Fairouz Tchier
Additional contact information
Haifa Bin Jebreen: Department of Mathematics, College of Science, King Saud University, Riyadh 11 551, Saudi Arabia
Fairouz Tchier: Department of Mathematics, College of Science, King Saud University, Riyadh 11 551, Saudi Arabia

Mathematics, 2020, vol. 9, issue 1, 1-13

Abstract: Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ -weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

Keywords: interpolating scaling functions; hyperbolic equation; Galerkin method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/1/78/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/1/78/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2020:i:1:p:78-:d:473124

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().