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Sturm Liouville Equation

  • Definition: A second-order ordinary differential equation d/(dx)[p(x)(dy)/(dx)]+[lambdaw(x)-q(x)]y=0, where lambda is a constant and w(x) is a known function called either the density or weighting function. The solutions (with appropriate boundary conditions) of lambda are called eigenvalues and the corresponding u_lambda(x) eigenfunctions. The solutions of this equation satisfy important mathematical properties under appropriate boundary conditions (Arfken 1985).

    Source: http://mathworld.wolfram.com

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