本文研究一类燃烧爆炸数学模型的有限差分解法.方程的指数源项刻画了Arrhenius反应速率,常用于模拟刚性点火过程.通过引入截断函数,原问题转化为具有一致有界连续解的近似模型.当截断常数充分大时,模型的爆破解和几乎完全爆破解可以通过求解近似系统获得,且求解过程不产生数值爆炸.适当优化步长选择,爆破位置和爆破时刻的逼近效果比直接离散原问题求解更简单,计算效果更好.最后,数值实验验证了理论分析的结果和模型的物理性质.“,”In this paper,we study an efficient finite difference method based on the uniform mesh for a class of semilinear parabolic equation arising from combustion process.Due to the capability of exponential source on simula-ting Arrhenius reactive rate,the considered model may theoretically describe the rigid ignition process in combustion.By introducing an indicator,the original equation is transformed to an approximate model with globally smooth solu-tion.When the cut-off level constant is sufficiently large,the solution of original equation can be obtained by solving the approximate model,without numerical blowup.By carefully choosing the step sizes,the bloup position and mo-ment can be computed more simply and efficiently.Finally,numerical simulations are provided to verify the mathe-matical analysis and physical properties of proposed blowup-combustion model.