Solve thermal explosion model by central difference and Newton iteration method

  • Xijian Wang Wuyi University
  • Tonghua Zeng Wuyi University
Keywords: Thermal explosion equation · Central difference method · Nonlinear system of equations · Newton iteration method · Convergence order


In 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.

Author Biographies

Xijian Wang, Wuyi University
School of Mathematics and Computational Science
Tonghua Zeng, Wuyi University
School of Mathematics and Computational Science


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.

How to Cite
Wang, X., & Zeng, T. (2015). Solve thermal explosion model by central difference and Newton iteration method. Statistics, Optimization & Information Computing, 3(2), 197-205.
Research Articles