Boundary-value problems that arise in practice often exhibit rapid growth and decline behaviour. The single interval discrete weighted residual method (Nouman and Schonbach 1977) approach may be inadequate for solving such boundary-value problems. This paper, therefore, is devoted to developing and illustratingmulti-intervaldiscrete weighted residual methods (DWRM's) for solving these numerically sensitive problems. The numerical difficulties associated with solving these boundary-value problems are reduced by dividing the problem interval into a number of sub-intervals and constructing the DWBM solution piecewise in each of these subintervals. Joining conditions are imposed at the interfaces of adjacent subintervals to piece together the individual solutions in each of the subintervals. The modal coefficients are evaluated as the solution of the combined DWRM and joining condition equations. Multi-interval DWRM's provide computationally efficient procedures for solving numerically sensitive boundary-value problems. This multi-interval viewpoint can also be applied to improve the numerical accuracy of other boundary-value problem solution techniques.