3 rd Numerical Solution of Energy Transmission Lines Equivalent Circuit Equations with Adomian Decomposition Method N.F. O. Serteller 1 , D. Ustundag 2 1 MarmaraUniversity, Electrical-Electronics Engineering, Goztepe, Istanbul, fserteller@marmara.edu.tr 2 Marmara University Art and Science Faculty Mathematics Department, Goztepe,Istanbul, dustundag@marmara.edu.tr In this study, analysis has been proposed for the mathematical model of the equivalent circuit to provide solu- tion of electrical energy power transmission lines (ETL) with Adomian Decomposition Method (Adomian Decom- pozition Method-ADM). By the help of Mathematica8 software program, these partial differential equations as a function of voltage (current) are solved and compared with the finite difference method (Finite element method- FDM) again developed with mathematica8 program. The results obtained from ADM and FDM was found in very good synchronism. To illustrate the method some examples are provided. The results showed the simplicity and the efficiency of the method. 1 Intoduction Since the first development of the transmission lines studies, numerous mathematical and experimental analyses have been done by researchers. Especially various mathematical analysis methods of ETL or telegraph equation are commonly used in the study of wave propagation of electric signals in a cable transmission line and also in wave phenomena by researchers [1, 2, 3, 4, 5]. Generally in ETL, resistance, capacitance and inductance occurs having less impact at low frequencies and with its increasing effect and distribution, as the frequency goes up. These are called distributed parameters. These in order are featured with R, C, L and G show line’s resistance, capacitance, inductance and conductance values per each unit length respectively [1, 2, 3, 4, 5]. 2 Mathematical Methods and Examples In this section, the equations known as telegraph equations and holding an importance in electric-electronic en- gineering are given by using two different methodology (ADM-FDM), graphically in three test examples. To determine the unknown in equations, depending on the source connected to transmission line and the effect of the load transmission line, the problems discussed are questioned whether in terms of two border conditions or two initial terms. By using initial values, the explicit solutions of telegraph equation for different particular cases have been derived. For FDM, 100 × 100 grid system is has been solved, then for ADM the formulas are done by finding the total of initial six terms. Solution is graphically presented in Figure1.