An unconditionally stable parallel difference scheme for telegraph equation. (English) Zbl 1181.78018

Summary: We use an unconditionally stable parallel difference scheme to solve telegraph equation. This method is based on the domain decomposition concept and uses asymmetric Saul’yev schemes for internal nodes of each sub-domain and the alternating group implicit method for interfacial nodes of the sub-domains. This new method has several advantages, such as: good parallelism, unconditional stability and better accuracy than the original Saul’yev schemes. The details of the implementation and the proof of stability are briefly discussed. Numerical experiments on stability and accuracy are also presented.


78M20 Finite difference methods applied to problems in optics and electromagnetic theory
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
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