Method for computer-aided prediction of the behavior of system described by differential equations, involves checking coefficient matrix for presence of elements different from zero

摘要

A method for numerically solving a linear equation system (A.x=b) with a computer program running on a computer, involves a quadratic coefficient matrix (A), an unknown vector (x) and an inhomogeneity vector (b). The coefficient matrix (A) is checked for the presence of elements different from zero, then a Markowitz product table is produced (M), in which for each row (i) and column (i) of the coefficient matrix (A), the product (pi = ri-1).(ci-1) is entered. The Markowitz product table is searched through and the residual matrix (r) is determined from those elements of the coefficient matrix (A) which are located in non-noted lines or non-noted columns. A complement matrix (B) is prepared from the residual matrix (R) according to a given relationship, and the remaining values of the complement matrix (B) are set to the value zero. The method is used for the complement matrix (B) for determining an elimination sequence of the diagonal elements of the complement matrix (B) and entry of the row numbers of the coefficient matrix (A) belonging to the diagonal elements of the complement matrix (B). The elimination- and substitution- methods are used for solving the equation (A.x=b).