We introduce a solver for stiff ordinary differential equations (ODEs) that is based on the deferred correction scheme for the corresponding Picard integral equation. Our solver relies on the assumption that the solution can be accurately represented by a combination of carefully selected complex exponentials. The solver’s accuracy and stability rely on the computation of highly accurate quadra...

Comparative studies of methods of reverse time migration (RTM) show that spectral methods for calculating the Laplacian impose the least stringent demands on discretization stepsize; thus with spectral methods, the grid reenements often required by other methods can be avoided. Implemented with absorbing boundary conditions , which are energy-tuned to give good absorption at the boundaries, the...

We consider a primal-dual algorithm for minimizing f(x) + h(Ax) with differentiable f . The primal-dual algorithm has two names in literature: Primal-Dual Fixed-Point algorithm based on the Proximity Operator (PDFPO) and Proximal Alternating Predictor-Corrector (PAPC). In this paper, we extend it to solve f(x) + h l(Ax) with differentiable l and prove its convergence under a weak condition (i.e...

In the context of solving nonlinear partial differential equations, Shu and Osher introduced representations of explicit Runge-Kutta methods, which lead to stepsize conditions under which the numerical process is totalvariation-diminishing (TVD). Much attention has been paid to these representations in the literature. In general, a Shu-Osher representation of a given Runge-Kutta method is not u...

This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its per-iterate convergence rate is analyzed. The novel part of the approach is in the choice of weights that are used to construct the averages. Through the use o...

In the literature, much attention has been paid to Runge-Kutta methods (RKMs) satisfying special nonlinear stability requirements indicated by the terms total-variation-diminishing (TVD), strong stability preserving (SSP) and monotonicity. Stepsize conditions, guaranteeing these properties, were derived by Shu and Osher [J. Comput. Phys., 77 (1988) pp. 439-471] and in numerous subsequent papers...

This paper deals with iterative gradient and subgradient methods with random feasibility steps for solving constrained convex minimization problems, where the constraint set is specified as the intersection of possibly infinitely many constraint sets. Each constraint set is assumed to be given as a level set of a convex but not necessarily differentiable function. The proposed algorithms are ap...

Most existing work uses dual decomposition and first-order methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This paper develops an alternative distributed Newton-type fast converging algorithm for solving NUM problems with self-concordant utility functions. By using novel matrix splitting techniques, bot...

Gradient projection (GP) algorithm has been shown as an efficient algorithm for solving the traditional traffic equilibrium problem with additive route costs. Recently, GP has been extended to solve the nonadditive traffic equilibrium problem (NaTEP), in which the cost incurred on each route is not just a simple sum of the link costs on that route. However, choosing an appropriate stepsize, whi...

in this paper, we consider the construction of a new class ofnumerical methods based on the backward differentiation formulas(bdfs) that be equipped by including two off--step points. werepresent these methods from general linear methods (glms) pointof view which provides an easy process to improve their stabilityproperties and implementation in a variable stepsize mode. thesesuperiorities are ...