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An effective linear scheme to solve nonlinear degenerate parabolic differential equations

✍ Scribed by M.S. El-Azab

Book ID
104352677
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
437 KB
Volume
46
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this paper, we consider the approximate solution of the following problem. Given R C RN (1 5 N 5 3), find u(z, t) such that &b(u) -Au. + P,Vu = 0, inQ=Rx (O,T), u = 0, onCzaRx(O,T), u(z, 0) = UO(I), vz ER, where the function b(s) is a monotonically increasing function satisfying 0 5 b' 5 co. To solve this problem, we introduce a new nonstandard time discretization scheme.

We prove stability and convergence results.

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An efficient algorithm to solve a sequence of linear equations arising in nonlinear H∞ control
✍ Jie Huang πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 615 KB

This paper proposes an efficient algorithm to solve a sequence of linear algebraic equations resulting from approximating the nonlinear H ~ control law by Taylor series. A characterization of the eigenstructure of a class of matrices that define the linear equations is first given. This characteriza