Chein-Shan Liu1
CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 85-112, 2010, DOI:10.3970/cmes.2010.056.085
Abstract We propose a novel technique, transforming the generalized SturmLiouville problem: w'' + q(x,λ)w = 0, a1(λ)w(0) + a2(λ)w'(0) = 0, b1(λ)w(1) + b2(λ)w'(1) = 0 into a canonical one: y'' = f, y(0) = y(1) = c(λ). Then we can construct a very effective Lie-group shooting method (LGSM) to compute eigenvalues and eigenfunctions, since both the left-boundary conditions y(0) = c(λ) and y'(0) = A(λ) can be expressed explicitly in terms of the eigen-parameter λ. Hence,
the eigenvalues and eigenfunctions can be easily calculated with better accuracy,
by a finer adjusting of λ to match the right-boundary condition y(1) =… More >
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