In this paper we control the first moment of the initial approximations and obtain the order of convergence and the asymptotic profile of a general solution by two explicit “canonical” approximations: a diffusive N-wave and a diffusion wave solution. The order of convergence of both approximations is O(t1/(2r)−3/2) in Lr norm, 1 ≤ r ≤ ∞, as t → ∞, which is faster than the well-known classical c...

The nonlinear transformations t o accelerate the convergence o f sequences due t o Levin are considered and bounds o n the errors are derived. Convergence theorems for oscillatory and some monotone sequences are proved.

Abstract. We investigate convergence of sequences of n × n matrix exponential functions t → etA k for t > 0, where Ak → A, Ak is nonsingular and A is nilpotent. Specifically, we address pointwise convergence, almost uniform convergence, and, viewing the exponential as a Schwartz distribution, weak∗ convergence. We show that simple results can be obtained in terms of the eigenvalues of A−1 k alo...

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

In this paper, we present a new method for solving Reproducing Kernel Space (RKS) theory, and iterative algorithm for solving Generalized Burgers Equation (GBE) is presented. The analytical solution is shown in a series in a RKS, and the approximate solution u(x,t) is constructed by truncating the series. The convergence of u(x,t) to the analytical solution is also proved.

This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for u′ t au t bu t . The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are ob...

This paper considers convex programs with a general (possibly non-differentiable) convex objective function and Lipschitz continuous convex inequality constraint functions. A simple algorithm is developed and achieves an O(1/t) convergence rate. Similar to the classical dual subgradient algorithm and the ADMM algorithm, the new algorithm has a parallel implementation when the objective and cons...

Systems _ x(t) = F(t; x(t); ") depending on a small parameter " are considered. We introduce a concept of convergence of such a system to a system _ x(t) = G(x(t)). Assuming this convergence, we prove that global asymptotic stability for _ x(t) = G(x(t)) implies some notion of \practical stability" for _ x(t) = F(t; x(t); ") if F(; x; ") satisses a periodicity assumption. We apply this theory t...

Influenced by Higham, Mao and Stuart [10], several numerical methods have been developed to study the strong convergence of the numerical solutions to stochastic differential equations (SDEs) under the local Lipschitz condition. These numerical methods include the tamed Euler–Maruyama (EM) method, the tamed Milstein method, the stopped EM, the backward EM, the backward forward EM, etc. In this ...

Let ( t )t∈R+ be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure π . We investigate the rates of convergence of the transition function P t (x, ·) to π ; specifically, we find conditions under which r(t)‖P t (x, ·)−π‖ → 0 as t → ∞, for suitable subgeometric rate functions r(t), where ‖ · ‖ denotes the usual total variation norm for a ...