There are many choices and combinations to be made when employing the ADE method and these pertain to both the method itself and to the PDE that it approximates. Some scenarios that we discussed in this appendix are: S1: Employ domain truncation or domain transformation. S2: PDE in conservative of non-conservative form. S3: Simplify the PDE by transforming its coefficients. S4: Barakat-Clark, Larkin and Saul'yev methods for diffusion. S5: Towler-Yang, Roberts-Weiss and upwinding for the convection. S6: Constant versus non-constant meshes. S7: Yanenko strategy for mixed derivatives. S8: Use of extrapolation methods. S9: Exponential fitting for convection-dominated problems.Having chosen for a particular PDE and associated ADE variant, we can consider testing the following activities: A1: Large expiry time (similar to an elliptic problem). A2: Convection dominance. A3: Analogous, simpler cases. A4: Choice of boundary conditions. A5: Correlation values in the closed range [-1, 1].Having an exact solution is ideal but not always possible and in these cases we can run two (or more) variants of ADE in parallel and compare the output. This process can be automated, thus freeing up developer time.Some useful Boost:.Random: generate the input parameters(e.g. Uniform).ublas: useful (See my FD2 post error analysis). multiarray: store n-dim data for later 'SQL SELECT' stuff.
Last edited by Cuchulainn
on August 12th, 2012, 10:00 pm, edited 1 time in total.