JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 55, No, 2, NOVEMBER 1987 A Nonasymptotic Method for General Linear Singular Perturbation Problems M. K. KADALBAJOO ~ AND Y. N. REDDY 2 Communicated by S. M. Roberts Abstract. The nonasymptotic method developed in Ref. 1 has been extended for solving general linear singularly perturbed two-point boun- dary-value problems. Firstly, we discuss problems with a right-hand boundary layer. Secondly, we discuss problems with an interior layer. Finally, we discuss problems with two boundary layers. Numerical experience with the method for some model problems is also reported to confirm the theoretical analysis. Key Words. Singular perturbations, ordinary differential equations, two-point boundary-value problems, boundary layers, interior layers, Simpson's rule. I. Introduction In ReL 1, we developed a nonasymptotic method for solving linear singularly perturbed two-point boundary-value problems with a left-hand boundary layer. The motivating impulse for this method was to provide the practicing engineer or applied mathematician with a means of solving a class of singular perturbation problems in a routine manner. The method avoided the principal problem of the conventional techniques, namely, finding the appropriate asymptotic expansion (see Ref. 2 for technique, designed for similar purposes). As part of a continuing effort to determine the applicability and the limitations of the nonasymptotic method, we have been attempting to solve general linear singularly perturbed two-point boundary-value problems in ordinary differential equations. Singular Assistant Professor, Department of Mathematics, Indian Institute of'Technology, Kanpur, India. 2 Research Scholar, Department of Mathematics, Indian Institute of Technology, Kanpur, India. 257 0022-3239/87/1100-0257505,00/0 • 1987 Plenum Publishing Corporation