Journal of Mathematical Physics · 1968 · 11 citations · 2 references
Natural SciencesMathematicsComputational MechanicsComputational PhysicsDifferential EquationsBoundary ConditionsBoundary-value ProblemsPartial Differential EquationsPerturbation MethodsPerturbation TheorySingular Perturbation TheoryAsymptotic ExpansionsAsymptotic PropertiesAsymptotic TheoryMatched Asymptotic ExpansionsNonlinear Boundary-value ProblemsSingular Perturbation AnalysisSingular Perturbations In Partial Differential EquationsSingularly Perturbed Boundary Value Problems
The asymptotic properties of a class of nonlinear boundary-value problems are studied. For large values of a parameter, the differential equation is of the singular-perturbation type, and its solution is constructed by means of matched asymptotic expansions. In two special cases, very simple approximate analytic solutions are obtained, and their accuracy is illustrated by showing their good agreement with the exact numerical solution of the problem.
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Lectures in Theoretical Physics
Wesley E. Brittin, B. W. Downs, Joanne Downs et al. · American Journal of Physics · 1962 · 3K citations