Finite Difference Schemes and Partial Differential Equations John Strikwerda
Publisher: SIAM: Society for Industrial and Applied Mathematics

Instead, you can try to implement a finite difference method. NDSolve switches between integration schemes based on the problem at hand, adapting step sizes and monitoring stiffness as it goes. One can test the accuracy of this method to the finite difference schemes. If you try to enter this elliptic PDE into NDSolve, Mathematica will vigorously protest. The numerical method I employ is 2 dimensional finite difference ADI scheme. However For example work on the the PDE of the transformation Price' = Price*h(v) with h a function that goes to zero quickly for v->vmax. The laplace transform of Black-Scholes PDE was taken and the result was inverted using the Talbot method for numerical inversion. As a consequence, the Operatively, theCFLcondition is commonly prescribed for those terms of the finite-difference approximation of general partial differential equations which model theadvection phenomenon.[5]. It arises when explicit time-marching schemes（显式时间推进计划，显式格式条件稳定和条件收敛，而隐式格式往往是无条件稳定和无条件收敛的，但是不容易求解数值解。）are used for the numerical solution. Advanced users can override these options, Consider the following PDE: We seek a solution, f(x,y) on the domain [0,10]x[0,10]. First, we will divide the domain into a grid.