Space-Time Collocation Method: Loop Quantum Hamiltonian Constraints

A space-time collocation method (STCM) using asymptotically-constant basis functions is proposed and applied to the quantum Hamiltonian constraint for a loop-quantized treatment of the Schwarzschild interior. Canonically, these descriptions take the form of a partial difference equation (PDE). The space-time collocation approach presents a computationally efficient, convergent, and easily parallelizable method for solving this class of equations, which is the main novelty of this study. Results of the numerical simulations will demonstrate the benefit from a parallel computing approach; and show general flexibility of the framework to handle arbitrarily-sized domains. Computed solutions will be compared, when applicable, to a solution computed in the conventional method via iteratively stepping through a predefined grid of discrete values, computing the solution via a recursive relationship.

• Publication year

  2020

• Venue

  International Journal of Modern Physics C

• Publication date

  2020-02-14

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1142/s0129183120501661arXiv 2002.06229
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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