相关论文: The renormalization method from continuous to disc…

This paper reports on recent work to compute the asymptotic solution of a n-th order ordinary differential equation. Symbolic methods are used to compute the asymptotics over a large region. Application is made to the computation of the…

The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…

By means of an updated renormalization method, we construct asymptotic expansions for unstable manifolds of hyperbolic fixed points in the double-well map and the dissipative H\'enon map, both of which exhibit the strong homoclinic chaos.…

Hyperasymptotics is an analytical method that incorporates exponentially small contributions into asymptotic approximations, thereby expanding their domain of validity, improving accuracy, and providing deeper insight into the underlying…

The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First…

Reformulated uniform asymptotic expansions are derived for ordinary differential equations having a large parameter and a simple turning point. These involve Airy functions, but not their derivatives, unlike traditional asymptotic…

In plasma simulations, where the speed of light divided by a characteristic length is at a much higher frequency than other relevant parameters in the underlying system, such as the plasma frequency, implicit methods begin to play an…

In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…

Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov…

We develop a new asymptotic method for the analysis of matrix Riemann-Hilbert problems. Our method is a generalization of the steepest descent method first proposed by Deift and Zhou; however our method systematically handles jump matrices…

In this note, two generalized corollaries to the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides. Lyapunov-based analysis methods are…

A general invariant manifold theorem is needed to study the topological classes of smooth dynamical systems. These classes are often invariant under renormalization. The classical invariant manifold theorem cannot be applied, because the…

In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…

In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of…

In Causal Perturbation Theory the process of renormalization is precisely equivalent to the extension of time ordered distributions to coincident points. This is achieved by a modified Taylor subtraction on the corresponding test functions.…

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…

We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…

We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…

In this work we present and discuss a possible globalization concept for Newton-type methods. We consider nonlinear problems $f(x)=0$ in $\mathbb{R}^{n}$ using the concepts from ordinary differential equations as a basis for the proposed…