that must be stored by the selected numerical method. For the purpose of illustrating the procedure the first n = 3 equations are: A code called RTBC was written in C which employed the LU Factorization package to solve the complex valued tri-diagonal system of simultaneous linear equations numerically. 12 In matrix form, n = 1 Ψ 1 imax − 1 − l (0) $_{imax}$Ψ 1 imax = − Ψ 0 imax − 1 = b $^{0}$( imax ) (43) n = 2 Ψ 2 imax − 1 − l (0) $_{imax}$Ψ 2 imax = l 1 $_{imax}$Ψ 1 imax − Ψ 1 imax − 1 = b $^{1}$( imax ) (44) n = 3 Ψ 3 imax − 1 − l (0) $_{imax}$Ψ 3 imax = l 2 $_{imax}$Ψ 1 imax + l 1 $_{imax}$Ψ 2 imax − Ψ 2 imax − 1 = b $^{2}$( imax ) (45)     C − 1 0 0 0 · · · − 1 C − 1 0 0 · · · 0 − 1 C − 1 0 · · · . . . . . . . . . . . . 0 0 · · · − 1 C − 1 0 0 0 · · · − 1 l (0) imax         Ψ n 2 Ψ n 3 Ψ n 4 . Ψ n imax − 1 Ψ n imax     =     b (2) b (3) b (4) . b ( imax − 1) b ( imax )     (46)