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The solution of the sparse algebraic system for a point controlled elliptic distributed parameter system by a multiple shooting and sweep algorithm is discussed. The multiple shooting and sweep algorithm enhances the convergence rate of the ordinary shooting method while achieving a significant reduction in the dimension of the linear equations to be solved. The optimization algorithm for a special problem involving the minimum cost selection of source intensities with the state satisfying a specified constraint set is presented. An application of the techniques involving the analysis and management design for water quality control in Corpus Christi Bay, an estuary on the Texas Gulf Coast in the United States, is discussed. The resulting algorithm is more than twice as fast as a corresponding successive overrelaxation method. (Author)