We present a novel solution method for It\^o stochastic differential equations (SDEs). We subdivide the time interval into sub-intervals, then we use the quadratic polynomials for the approximation between two successive intervals. The main properties of the stochastic numerical methods, e.g. convergence, consistency, and stability are analyzed. We test the proposed method in SDE problem, demonstrating promising results.

翻译：我们提出了一种求解伊藤随机微分方程的新方法。该方法将时间区间划分为若干子区间，并在相邻区间间使用二次多项式进行近似。我们分析了该随机数值方法的主要性质，如收敛性、相容性与稳定性。通过在随机微分方程问题上的测试，该方法展现了良好的性能表现。