Related papers: Existence and optimality of strong stability prese…
The objective of this paper is to prove the convergence of a linear implicit multi-step numerical method for ordinary differential equations. The algorithm is obtained via Taylor approximations. The convergence is proved following the…
Stabilized explicit methods are particularly efficient for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they loose their efficiency when a severe stiffness is induced by…
In this paper we consider the existence of positive solutions for a singular elliptic problem involving an asymtotically linear nonlinearity and depending on one positive parameter. Using variational methods, together with comparison…
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The…
We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…
We give a strongly polynomial time algorithm which determines whether or not a bivariate polynomial is real stable. As a corollary, this implies an algorithm for testing whether a given linear transformation on univariate polynomials…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…
Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the…
In this work we present two particular cases of the general duality result for linear optimisation problems over signed measures with infinitely many constraints in the form of integrals of functions with respect to the decision variables…
We study the convergence rate of a class of linear multi-step methods for BSDEs. We show that, under a sufficient condition on the coefficients, the schemes enjoy a fundamental stability property. Coupling this result to an analysis of the…
We introduce a new $\mathbf F$-modulated energy stability framework for general linear multistep methods. We showcase the theory for the two dimensional molecular beam epitaxy model with no slope selection which is a prototypical gradient…
Variable steps implicit-explicit multistep methods for PDEs have been presented in [17], where the zero-stability is studied for ODEs; however, the stability analysis still remains an open question for PDEs. Based on the idea of linear…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…
We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability…
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…
Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
In this work we study the stability regions of linear multistep or multiderivative multistep methods for initial-value problems by using techniques that are straightforward to implement in modern computer algebra systems. In many…