A new decoupling technique for the Hermite cubic collocation equations arising from boundary value problems

Wayne R. Dyksen and Robert E. Lynch

Mathematics and Computers in Simulation (MATCOM), 2000, vol. 54, issue 4, 359-372

Abstract: We present a new decoupling technique for solving the linear systems arising from Hermite cubic collocation solutions to boundary value problems with both Dirichlet and Neumann boundary conditions. While the traditional approach yields a linear system of order 2N×2N with bandwidth 2, our technique decouples this system into two systems, one with a tridiagonal system of order N−1×N−1 and the other with the identity matrix of order N×N. Besides cutting the work in half, our new approach results in a new tridiagonal system that exhibits the same desirable properties (e.g. symmetric, positive definite) as in the case of finite difference approximations. We validate our theoretical work with a number of experimental results, demonstrating both accuracy and stability.

Keywords: Elliptic boundary value problems; Hermite cubic collocation (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:54:y:2000:i:4:p:359-372

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