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 $T \to 0$ 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