SPECTRAL PROPERTIES OF DERIVATIVE OPERATORS IN THE BASIS-SPLINE COLLOCATION METHOD

J.C. Wells, V.E. Oberacker, M.R. Strayer and A.S. Umar
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J.C. Wells: Center for Computationally Intensive Physics, Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831–6373, USA
V.E. Oberacker: Center for Computationally Intensive Physics, Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831–6373, USA
M.R. Strayer: Center for Computationally Intensive Physics, Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831–6373, USA
A.S. Umar: Center for Computationally Intensive Physics, Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831–6373, USA

International Journal of Modern Physics C (IJMPC), 1995, vol. 06, issue 01, 143-167

Abstract: We discuss the basis-spline collocation method for the lattice solution of boundary-value differential equations, drawing particular attention to the difference between lattice and continuous collocation methods. Spectral properties of the basis-spline lattice representation of the first and second spatial derivatives are studied for the case of periodic boundary conditions with homogeneous lattice spacing and compared to spectra obtained using traditional finite-difference schemes. Basis-spline representations are shown to give excellent resolution on small-length scales and to satisfy the chain rule with good fidelity for the lattice-derivative operators using high-order splines. Application to the one-dimensional Dirac equation shows that very high-order spline representations of the Hamiltonian on odd lattices avoid the notorious spectral-doubling problem.

Keywords: Basis-splines; Collocation Method; Lattice Techniques; Dirac Equation (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1142/S0129183195000125

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