AI 中文总结
该研究针对抛物型方程，推导了变步显式两步指数Adams方法的最优阶后验误差估计，通过引入带二阶残差的近似重构实现最优阶估计，并经数值实验验证了方法的收敛阶与自适应算法的高效性。
AI 中文摘要
本文推导了抛物型问题变步长显式两步指数Adams（E-Adams2）方法的最优阶后验误差估计。首先引入由分段线性近似解定义的E-Adams2近似，该近似会导致次优误差估计。为恢复最优阶误差估计，我们对显式E-Adams2方法引入了带有二阶残差的适当近似重构，该重构在推导所提显式线性与半线性抛物型方程方法的最优阶后验误差估计中发挥关键作用。开展了各类数值实验，以验证后验量的正确收敛阶及自适应算法的高效性。
英文摘要
In this paper, we derive optimal order a posteriori error estimates for the variable step-size explicit two-step exponential Adams (E-Adams2) method for parabolic problems. We begin by introducing an E-Adams2 approximation, deffned by the piecewise linear approximate solutions, which leads to suboptimal error estimates. To recover optimal order error estimates, we introducean appropriate reconstruction of the approximation with the second order residual for the explicit E-Adams2 method, which plays key roles in deriving optimal order a posteriori error estimates for the proposed explicit method for linear and semilinear parabolic equations. Various numerical experiments are carried out to verify the correct convergence rates of the a posteriori quantities, and the high efffciency of the adaptive algorithm.
