ABSTRACT
Equation (10.70) comprises a tridiagonal system of linear algebraic equations. That system of equations may be written as
Afn+1 = b (10.71) where A is the (imax - 2 x imax - 2) coefficient matrix, fn+1 is the (imax - 2 x I) solution column vector, and b is the (imax - 2 x I) column vector of nonhomogeneous terms. Equation (10.71) 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 even further.
