Error Estimates for the Solution of the Radial Schr?dinger Equation by the Rayleigh--Ritz Finite Element Method |
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| Authors: | SCHOOMBIE S W; BOTHA J F |
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| Institution: |
Department of Applied Mathematics, University of the Orange Free State P.O. Box 339, Bloemfontein 9300, Republic of South Africa
Institute of Ground Water Studies, University of the Orange Free State P.O. Box 339, Bloemfontein 9300, Republic of South Africa
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| Abstract: | Approximate eigenvalues and eigenfunctions are obtained forthe radial Schr?dinger equation by applying the Rayleigh—Ritzmethod to a function space consisting of polynomial splinesof odd degree. Computable a posteriori error estimates for theeigenfunction error estimates are obtained. The sharpness ofthese estimates is illustrated for the harmonic oscillator andWoods—Saxon potentials, using both cubic splines and piecewisecubic Hermite polynomials. |
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