A second-order accurate and unconditionally energy stable numerical scheme for nonlinear sine-Gordon equation. (English) Zbl 07845451
Summary: In this work, a second-order finite difference method is proposed to solve a nonlinear sine-Gordon equation. The constructed implicit scheme is proved to be unconditionally energy stable. A linear iteration algorithm is used to solve this nonlinear numerical scheme, and we prove that this iteration algorithm is convergent with a negligible constraint for time step. By constructing a suitable high-precision numerical solution, and using the inverse inequality and refinement constraint \(\Delta t \leq Ch\), the error estimate in \(L^\infty (0, T; L^\infty)\) norm of the fully discrete scheme is obtained. Several numerical examples are given to confirm the sharpness of our theoretical analysis.
MSC:
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 35Qxx | Partial differential equations of mathematical physics and other areas of application |
| 65Nxx | Numerical methods for partial differential equations, boundary value problems |
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