A novel shifted Vieta–Lucas spectral collocation approach for multidimensional generalized Benjamin–Bona–Mahony–Burgers equations
Ramy M. Hafez, Hany Mostafa Ahmed, Alhanouf Alburaikan, Moodi Abdulrhman Abdullah Alrajeh, Hamiden Abd El-Wahed Khalifa · 2026
Read A novel shifted Vieta–Lucas spectral collocation approach for multidimensional generalized Benjamin–Bona–Mahony–Burgers equations by Ramy M. Hafez, Hany Mostafa Ahmed, Alhanouf Alburaikan, Moodi Abdulrhman Abdullah Alrajeh, Hamiden Abd El-Wahed Khalifa (2026) in the Tower of Babel, a free online library of public-domain works preserved in clean, searchable text. No sign-up. The full text is served as a plain-text file at a predictable URL, where text is present: https://antarctic-labs.com/tower-of-babel/pmc-13156290.txt.
Description
Waves that spread while also dispersing, common in shallow water and plasma, follow equations too tangled for pen-and-paper answers in two dimensions. Ramy Hafez, Hany Ahmed, Alhanouf Alburaikan, Moodi Alrajeh, and Hamiden Khalifa present a numerical recipe for a family of such equations in this 2026 paper. Their method expands the unknown wave as a short sum of special polynomials, shifted Vieta-Lucas functions, and forces the equation to hold at chosen points.
That turns the wave problem into algebra a computer can solve fast. The authors prove the scheme converges and bound its error, then run tests in one and two space dimensions. Results beat earlier methods on accuracy while staying simple to run. They pitch the recipe as a stable, general tool for nonlinear wave equations across applied science.
Catalog record
| CREATOR | Ramy M. Hafez, Hany Mostafa Ahmed, Alhanouf Alburaikan, Moodi Abdulrhman Abdullah Alrajeh, Hamiden Abd El-Wahed Khalifa |
|---|---|
| YEAR | 2026 |
| COLLECTION | PAPERS |
| FORMAT | TXT |
| FILE SIZE | 147 KB |
| VERSION | 1.0 |
| LICENSE | CC BY 4.0 |
| RIGHTS | CC BY |
| SOURCE | Europe PMC |