Convergence analysis of a linearized Crank–Nicolson scheme for the two‐dimensional complex Ginzburg–Landau equation
Y Zhang, Z Sun, T Wang - Numerical Methods for Partial …, 2013 - Wiley Online Library
Y Zhang, Z Sun, T Wang
Numerical Methods for Partial Differential Equations, 2013•Wiley Online LibraryA linearized Crank–Nicolson‐type scheme is proposed for the two‐dimensional complex
Ginzburg–Landau equation. The scheme is proved to be unconditionally convergent in the
L2‐norm by the discrete energy method. The convergence order is article mathrsfs amsmath
empty O (τ^ 2+ h_1^ 2+ h^ 2_2), where τ is the temporal grid size and h1, h2 are spatial grid
sizes in the x‐and y‐directions, respectively. A numerical example is presented to support
the theoretical result.© 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq …
Ginzburg–Landau equation. The scheme is proved to be unconditionally convergent in the
L2‐norm by the discrete energy method. The convergence order is article mathrsfs amsmath
empty O (τ^ 2+ h_1^ 2+ h^ 2_2), where τ is the temporal grid size and h1, h2 are spatial grid
sizes in the x‐and y‐directions, respectively. A numerical example is presented to support
the theoretical result.© 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq …
A linearized Crank–Nicolson‐type scheme is proposed for the two‐dimensional complex Ginzburg–Landau equation. The scheme is proved to be unconditionally convergent in the L2‐norm by the discrete energy method. The convergence order is article mathrsfs amsmath empty O (τ^ 2+ h_1^ 2+ h^ 2_2), where τ is the temporal grid size and h1, h2 are spatial grid sizes in the x‐and y‐directions, respectively. A numerical example is presented to support the theoretical result.© 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
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