SIAM Journal on Applied Mathematics · 1985 · 78 citations · 6 references
Natural SciencesMathematicsPhysicsComputational MechanicsDifferential EquationsFluid DynamicsBoundary-value ProblemsDifference EquationsNumerical Methods For Differential EquationsPerturbation MethodsPerturbation TheorySingular Perturbation TheoryLinear Difference EquationsPerturbation AnalysisResonanceResonance BehaviorSecond-order Differential EquationsSingular Perturbation AnalysisTransition RegionsTurning Point Problems
This paper continues a study of a class of boundary-value problems for linear second-order differential-difference equations in which the second-order derivative is multiplied by a small parameter (SIAM J. Appl. Math., 42 (1982), pp. 502–531; 45 (1985), pp. 687–707). The previous papers focused on problems involving boundary and interior layer phenomena, rapid oscillations, and resonance behavior. The problems studied here have solutions which exhibit turning point behavior, i.e., transition regions between rapid oscillations and exponential behavior. The presence of the shift terms can induce large amplitudes and multiphase behavior over parts of the interval. A combination of exact solutions, singular perturbation methods, and numerical computations are used in these studies.
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Handbook of Mathematical Functions
Donald A. McQuarrie · American Journal of Physics · 1966 · 40.9K citations