A reduced-order extrapolated finite difference iterative scheme for uniform transmission line equation

In order to find the numerical solutions of the two-dimensional (2D) uniform transmission line equation, we first establish a fully second-order finite difference (FD) scheme in matrix-form and analyze the stability and convergence of the FD solutions by matrix analysis. Then we employ a proper orthogonal decomposition (POD) method to establish a reduced-order extrapolated FD (ROEFD) scheme containing very few unknowns for the 2D uniform transmission line equation and also make use of the matrix analysis to analyze the stability and convergence for the ROEFD solutions. Finally, we employ some numerical experiments to validate the effectiveness of the ROEFD scheme.