Abstract
In this paper, a novel linear equation solution method is proposed based on a row elimination back-substitution method (REBSM). The elimination and back-substitution procedures are carried out on individual row levels. The advantage of the proposed method is that it is much faster and requires less storage than the Gaussian elimination algorithm and, therefore, is capable of solving larger systems of equations. The method is particularly efficient for solving band diagonal sparse systems with symmetric or nonsymmetric coefficient matrices, and can be easily applied to popular numerical methods, such as the finite element method and the boundary element method. Detailed Fortran codes and examples are given to demonstrate the robustness and efficiency of the proposed method.
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