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

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  • Dyksen, Wayne R.
  • Lynch, Robert E.

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.

Suggested Citation

  • Dyksen, Wayne R. & Lynch, Robert E., 2000. "A new decoupling technique for the Hermite cubic collocation equations arising from boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(4), pages 359-372.
    • Handle: RePEc:eee:matcom:v:54:y:2000:i:4:p:359-372
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    Cited by:

    1. Marasi, H.R. & Derakhshan, M.H., 2023. "Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 368-389.
    2. Arora, Shelly & Kaur, Inderpreet, 2018. "Applications of Quintic Hermite collocation with time discretization to singularly perturbed problems," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 409-421.

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