中文摘要：

本文引入了求解二阶拟线性抛物型微分方程初值问题的一类新的数值算法一分层方法,这种数值方法是通过弱显式欧拉法离散其方程解的概率表示而得到的,相应地给出了该分层方法的收敛性结果.此外,还构造了基于插值的数值算法,最后提供了数值实验,得到的数值结果验证了获得的算法的精确性和有效性.

英文摘要：

This paper proposes a class of new layer methods for solving the initial value problems（IVPs） for second-order quasilinear parabolic equations, which is derived from using weak Euler scheme to discretisize probabilistic representation of the solution. Correspondly, we give the convergence results of such methods. Also,we construct the numerical algorithm based on interpolation. At last, some numerical tests are presented,and the numerical results validate the accuracy and validity of the obtained algorithm.