Fast Calculation Method for Transient Response of Transmission Line Based on Chebyshev Pseudospectral–Two-Step Three-Order Boundary Value Coupled Method

A Chebyshev pseudospectral–two-step three-order boundary value coupled method is proposed and presented for handling the issue associated with complicated calculation, low precision, and poor stability in the process of transient response of transmission line. The first order differential equation in time domain is obtained via dispersing the telegraph equation in space domain by utilizing the pseudospectral method (PSM) based on Chebyshev polynomial. Then the two-step three-order boundary value method (BVM3) is presented and employed to resolve the obtained differential equation, so the numerical solution of the space discrete points can be obtained. Furthermore, the Chebyshev pseudospectral–two-step three-order boundary value coupled method (PSM-BVM3) is presented and compared with the Chebyshev pseudospectral–two-step two order boundary value coupled method (PSM-BVM2), the pseudospectral–differential quadrature method (PSM-DQM), and the pseudospectral method–trapezoid rule (PSM-TR) to validate the feasibility of the new proposed method. Theoretical analysis and numerical simulation reveal that the proposed Chebyshev PSM-BVM3 has a higher performance than the conventional method. For the proposed Chebyshev PSM-BVM3, the higher precision, efficiency, and numerical stability can be obtained and achieved only with fewer discrete points in the space domain, which is suitable for solving the transient response of transmission line. The proposed PSM-BVM3 can improve the drawback of numerical instability of the PSM and can also improve the disadvantage of the BVM as it is not easy to change the latter’s timestep size.