A PIECEWISE LUCAS COLLOCATION METHOD FOR A DELAYED WILDFIRE MODEL
16th International Azerbaijan Congress on Life, Engineering, Mathematical, and Applied Sciences, Baku, Azerbaijan, 20 - 22 September 2026, pp.498-507, (Full Text)
- Publication Type: Conference Paper / Full Text
- City: Baku
- Country: Azerbaijan
- Page Numbers: pp.498-507
- Dokuz Eylül University Affiliated: Yes
Abstract
A reduced nonlinear delay differential equation (DDE) model is proposed for wildfire evolution under
delayed and time-dependent suppression. The model couples normalized fire intensity, combustible fuel,
effective suppression capacity, and a cumulative fire-impact index through a fire-memory delay and a
suppression-response delay. To handle delay- and event-induced losses of regularity, a low-degree
piecewise Lucas polynomial collocation scheme on delay- and event-aligned subintervals is developed.
For the nonlinear verification problem, the piecewise scheme with 𝑁𝑁 = 6 and ℎ = 0.25 attains a
maximum error of 1.09 × 10−9, whereas Newton iteration for the global Lucas expansion does not
converge at 𝑁𝑁 = 12. A 768-case ignition-phase–suppression-delay experiment, computed with a
verified RK4 method-of-steps solver, shows that under a synthetic day–night availability cycle the effect
of suppression delay depends on the ignition phase; over a 6-h horizon the integrated fire intensity varies
by a factor of 3.086 across the design grid. The results are synthetic-design outcomes rather than
calibrated estimates for a specific wildfire event.