Propounding statement of Patel Numerical Method for solution of an algebraic equation and simultaneous algebraic equations, both linear and non-linear, is presented. Also presented is Exactly formulated, and Accurately and Reliably convergent Incremental Gauss-Seidel Loadflow (EARIGSL). A new class of Loadflow Methods are invented. These invented Loadflow Methods are Y-matrix based coefficient matrix Patel Loadflow (CPL), its hybrid version HCPL, Patel Loadflow-1 (PL-1), PL-2, Patel Super Decoupled Loadflow (PSDL-YY), its hybrid version HPSDL-YY, Sparse Z-matrix based Patel Loadflow {SZPL or S[C]−1 PL (SCIPL)}, its hybrid version HSZPL or HCIPL, and Sparse Z-matrix could be real or complex and it can be derived from fully inverted coefficient matrix [C] or Jacobian matrix [J] or their different variants. A method of convergence data analytics based determining acceleration factor is also presented. Techniques developed in this application are applicable in other subjects or problems requiring solution of linear or nonlinear simultaneous algebraic equations.