Runge Kutta Chebyshev Method for parabolic ... - Brown University

Introduction Properties Pros and Cons Examples References
Stability boundary
According to the consistency condition, Pj(z) approximates e cjz
for z → 0 as
Pj = 1 + cjz + Xjz 2 + O(z 3 ). (26)
The choice of the stability function Pj(z) is the cental issue in
developing the RKC methods.
Stability Region S = {z ∈ C : |Ps| � 1}
Stability Boundary β(s) = max{−z : z � 0, |Ps| � 1}
Design rules: