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American Institute of Aeronautics and Astronautics

    Course Outline

    Perturbation Methods in Science and Engineering


    Course Outline:

    I. Introduction, Classification, and Advantages of Perturbation Methods
    A. Landau gauge orders and series expansions
    B. Systematic solution of transcendental equations

    II. Regular Perturbation Methods
    A. Regular expansion series and Bürmann’s inverse approach
    B. Successive approximations and the method of ansatz
    C. Dimensional analysis and scaling
    D. The von Karman and Laplace equations

    III. Rayleigh-Janzen Expansion Technique

    IV. Singular Perturbation Methods
    A. Identification of secular terms and singular behavior
    B. Construction of uniformly valid approximations

    V. Strained Coordinate Expansion (SCE) Techniques
    A. Lindstedt’s method of stretched coordinates
    B. PLK’s method of deformed coordinates
    C. Pritulo’s method of renormalization

    VI. Matched Asymptotic Expansion (MAE) Technique
    A. Treatment of boundary layers and inner/outer approximations
    B. Distinguished limits; Prandtl’s and Van Dyke’s matching principles
    C. Uniformly valid composite solutions

    VII. Multiple Scales Expansion (MSE) Technique
    A. Slow and fast scales
    B. Stretched and compressed scales

    VIII. WKB Technique

    IX. Van der Pol’s Method of Averaging

    X. Latta’s Method of Composite Expansions (MCE)

    XI. Adomian Decomposition (ADM) and Homotopy Analysis Method (HAM)

    XII. Asymptotic Expansion of Integrals:
    A. Laplace’s Method
    B. Watson’s Lemma