_ 1/2+1 - 2Yi +Y_1 d2 ,Tx7 : x)2	 • For the boundary point at i = 1, the forward-difference approximation to the derivative is used, which gives u2 -u1 (k(x)d no simplification was made and all the terms involved are taken into account. Further, because there is no coupling at the edges, the longitudinal stiffness coupling coefficient

doi:10.1201/9781482276237-62

Chapter

ABSTRACT

This matrix is sparse and band-diagonal (band = 5). The matrix does not require storage of order N2; instead, storage of order N is adequate. To obtain the solution, first, matrix A is factorized as A = PLQ, where P is a permutation matrix, L is a lower triangular matrix with at most two non-zero sub-diagonal elements per column, and Q is an upper triangular band matrix with four super-diagonals. The factorization is obtained by Gaussian elimination with partial pivoting. After factorization, the solution vector is calculated for different values of w. The computation time required is of order N.