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In this paper we develop a new β-method applied to the resolution of homogeneous transmission lines. A comparison with conventional methods used for this type of problems like FDTD method or classical β-method is also given. Furthermore, various numerical experiments are presented to confirm the accuracy, efficiency and stability of our proposed method. In particular, these simulations show that our new scheme is unconditionally stable and fourth-order accurate in space and time.

Numerical Analysis of Transmission Lines Equation by new β-method Schemes