Fully discrete approximation by Galerkin Runge-Kutta methods for quasilinear parabolic systems
Etsushi Nakaguchi, Atsushi Yagi · Hokkaido Mathematical Journal · 2002
We study fully discrete approximation of quasilinear parabolic systems.Pre- senting a full discretization scheme based on the Galerkin and the Runge-Kutta methods, we establish the stability and the error estimate of the scheme by means of the semigroup method.First our results are stated for a chemotaxis-growth system arising in biology, then those are generalized to quasilinear abstract parabolic evolution equations.