ABSTRACT
Equation (11.62) is a tridiagonal sysem of linear equations. That system of equations may be written as
(11.63) where A is the (imax - 2) x (imax - 2) coefficient matrix, fn+1 is the (imax - 2) x 1 solution column vector, and b is the (imax - 2) x 1 column vector of nonhomogeneous terms. Equation (11.63) can be solved very efficiently by the Thomas algorithm presented in Section 1.5. Since the coefficient matrix A does not change from one time level to the next, LU factorization can be employed with the Thomas algorithm to reduce the computational effort ever further. As shown in Section 1.5, once the LU factorization has been performed, the number of multiplications and divisions required to solve a tridiagonal system of linear equations by the Thomas algorithm is 3n, where n = (imax - 2) is the number of equations.
