14,351 research outputs found
An explicit predictor-corrector solver with applications to Burgers' equation
Forward Euler's explicit, finite-difference formula of extrapolation, is used as a predictor and a convex formula as a corrector to integrate differential equations numerically. An application has been made to Burger's equation
Phase transition between non-extremal and extremal Reissner-Nordstr\"om black holes
We discuss the phase transition between non-extremal and extremal
Reissner-Nordstr\"om black holes. This transition is considered as the
limit of the transition between the non-extremal and near-extremal
black holes.
We show that an evaporating process from non-extremal black hole to extremal
one is possible to occur, but its reverse process is not possible to occur
because of the presence of the maximum temperature.
Furthermore, it is shown that the Hawking-Page phase transition between small
and large black holes unlikely occurs in the AdS Reissner-Nordstr\"om black
holes.Comment: 12 pages, 6 figures, version to appear in MPL
Numerical solutions of nonlinear STIFF initial value problems by perturbed functional iterations
Numerical solution of nonlinear stiff initial value problems by a perturbed functional iterative scheme is discussed. The algorithm does not fully linearize the system and requires only the diagonal terms of the Jacobian. Some examples related to chemical kinetics are presented
Nonlinear grid error effects on numerical solution of partial differential equations
Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly
Numerical modeling of D-mappings with applications to chemical kinetics
Numerical modeling of D-mappings was studied and applied to solving nonlinear stiff systems. These mappings were locally linearized for convergence analysis, and some applications were made to chemical kinetics. The technique avoids using multistep implicit codes that require inversion of Jacobian matrices, but depends on the Jacobians for its convergence analysis
Normal variation for adaptive feature size
The change in the normal between any two nearby points on a closed, smooth
surface is bounded with respect to the local feature size (distance to the
medial axis). An incorrect proof of this lemma appeared as part of the analysis
of the "crust" algorithm of Amenta and Bern
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