Solve thermal explosion model by central difference and Newton iteration method
AbstractIn this paper, the general equation form of a thermal explosion in a vessel with boundary values is firstly presented, later the central difference method and Newton iteration method are used to solve the relevant partial differential equations in one-dimensional and two-dimensional forms, finally the order of convergence of the numerical scheme is verified by numerical experiments and the experiment results are provided.
N. Nikolaevich Semenov, Some problems of chemical kinetics and reactivity, Elsevier, vol. 2, 1959.
IA Zeldovich, G Io Barenblatt, VB Librovich, and GM Makhviladze, Mathematical theory of combustion and explosions, Consultants Bureau, New York, NY, 1985.
DA Frank-Kameneetıskiæi, Diffusion and heat transfer in chemical kinetics, Plenum Press, New York, vol. 2, 1969.
OM Todes and PV Melent’ev, Theory of thermal explosion. Part II. thermal explosion for unimoleclar reactions, Z. Fiz. Khim, vol. 13, pp. 1594–1609, 1939.
AG Merzhanov and FI Dubovitsky, The modern state of the theory of thermal explosion, Uspekhi Khimii, vol. 35, no. 4, 1966.
BF Gray, Critical behaviour in chemically reacting systems: Iiłan exactly soluble model, Combustion and Flame, vol. 20, no. 3, pp. 317–325, 1973.
Robert MM Mattheij, Sjoerd W Rienstra, and Jan HM ten Thije Boonkkamp, Partial differential equations: modeling, analysis, computation, Siam, 2005.
Peter Deuflhard, Newton methods for nonlinear problems: affine invariance and adaptive algorithms, Springer, vol. 35, 2011.
Carl T Kelley, Solving nonlinear equations with Newton’s method, Siam, vol. 1, 2003.
James M Ortega and Werner C Rheinboldt, Iterative solution of nonlinear equations in several variables, Siam, vol. 30, 2000.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).