The combination of Approximate Matrix Factorization (AMF), W-methods and iterative refinement in the solution of linear systems leads to the definition of AMFR-W-methods. This method class provides stable and accurate time integrators for parabolic PDEs with mixed derivatives discretized in space by means of Finite Differences (or Finite Volumes) in an arbitrary number of spatial dimensions. When the coefficients of the PDE actually depend on the spatial variables, the approximation of the pure diffusion coefficients by its respective maximum value produces simplified AMFR-W-methods requiring only a reduced number of LU decompositions of banded matrices with small bandwidth. The new class of methods is shown to be unconditionally stable regardless of the spatial dimension on a linear test problem relevant for homogeneous or periodic boundary conditions. Furthermore, high orders of convergence in PDE sense are observed when homogeneous boundary conditions are assumed. For general Robin boundary conditions, a simple algorithm is provided to convert a PDE problem into one where such conditions are homogeneous. Numerical experiments with the new simplified AMFR-W-methods on a linear parabolic problem with variable coefficients and the Heston problem from financial option pricing are presented.

线性系统解中近似矩阵分解（AMF），W方法和迭代精化的结合导致了AMFR-W方法的定义。此类方法为抛物线型PDE提供了稳定且准确的时间积分器，其混合衍生物通过任意数量的空间维中的有限差分（或有限体积）在空间中离散。当PDE的系数实际上取决于空间变量时，纯扩散系数通过其相应的最大值进行逼近会生成简化的AMFR-W方法，该方法仅需要减少带宽较小的带状矩阵的LU分解。在与均质或周期性边界条件相关的线性测试问题上，无论空间尺寸如何，新型方法都显示出无条件稳定。此外，当假设齐次边界条件时，可以观察到PDE意义上的高收敛性。对于一般的Robin边界条件，提供了一种简单的算法将PDE问题转换为此类条件是均质的。提出了使用新的简化AMFR-W方法对具有可变系数的线性抛物线问题和金融期权定价的Heston问题进行的数值实验。提供了一种简单的算法，将PDE问题转换为此类条件是均质的。提出了使用新的简化AMFR-W方法对具有可变系数的线性抛物线问题和金融期权定价的Heston问题进行的数值实验。提供了一种简单的算法，将PDE问题转换为此类条件是均质的。提出了使用新的简化AMFR-W方法对具有可变系数的线性抛物线问题和金融期权定价的Heston问题进行的数值实验。