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Linearly implicit time discretization of nonlinear parabolic equations. (English) Zbl 0834.65092
The authors consider linearly implicit one-step methods for time- discretization of linear and nonlinear parabolic differential equations. Stability results and several error estimates with different approximation orders are proven for the Rosenbrock methods and the \(W\)- methods where the last ones do not require the exact Jacobian of the problem. Remarks on the convergence order of the extrapolated linearly implicit Euler method are given.
The parabolic equations are studied in a Hilbert space framework. Several examples are considered, e.g., semilinear and quasilinear parabolic equations and stiff reaction-diffusion equations. The paper contains no numerical results.

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations
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