Document Zbl 1208.65126

High order compact alternating direction implicit method for the generalized sine-Gordon equation. (English) Zbl 1208.65126

J. Comput. Appl. Math. 235, No. 3, 837-849 (2010).

A high order linearized alternating direction implicit method (ADI) for the generalized sine-Gordon equation is proposed. Two techniques, ADI and linearization are used to solve the resulting nonlinear problem. The convergence rate of the second order in time and of the fourth order in space is proved. The numerical results confirm the theoretical ones.

Reviewer: Iwan Gawriljuk (Eisenach)

Cited in 41 Documents

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
35Q40	PDEs in connection with quantum mechanics
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

sine-Gordon equation; high-order finite difference scheme; error estimate; alternating direction implicite method; ADI method; linearization; convergence; numerical results

Software:

PDE2D

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Full Text: DOI

References:

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