Abstract
Diagonalized Legendre spectral methods for solving second-order eigenvalue problems are proposed. A new class of basis functions are constructed by using the matrix decomposition technique, which are simultaneously orthogonal in both L2- and H1-inner products, and lead to diagonal systems for second-order eigenvalue problems with constant coefficients. Numerical experiments show that the suggested approaches possess high-order accuracy and greatly improve the efficiency. Compared with the classical methods, the new methods simplify the calculation process, reduce the amount of calculation, and can effectively avoid the curse of dimensionality of high-dimensional eigenvalue problems.
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