Runge Kutta Chebyshev Method for parabolic ... - Brown University
Runge Kutta Chebyshev Method for parabolic ... - Brown University
Runge Kutta Chebyshev Method for parabolic ... - Brown University
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Introduction Properties Pros and Cons Examples References<br />
Consistency conditions<br />
Suppose Un = U(tn), where U(t), t � tn is a sufficiently<br />
smooth solution. All Yj satisfy an expansion<br />
Yj = U(tn) + cjτ ˙U(tn) + Xjτ 2 U (2) (tn) + O(τ 3 ) (13)<br />
Substitute this into the RKC <strong>for</strong>mula, we have<br />
X0 = X1 = 0, (14)<br />
Xj = µjXj−1 + νjXj−2 + ˜µjcj−1 (2 � j � s) (15)
Change language