Related papers: Algebraic Structures and Stochastic Differential E…

In this work, we analyse the discretisation of a recently proposed new Lagrangian approach to optimal control problems of affine-controlled second-order differential equations with cost functions quadratic in the controls. We propose exact…

This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…

Using complex analysis techniques we obtain precise asymptotic approximations for the kernels corresponding to the symmetric $\alpha$-stable processes and their fractional derivatives. We apply our method to general L\'evy processes whose…

This contribution presents an integration method based on the Simpson quadrature. The integrator is designed for finite-dimensional nonlinear mechanical systems that derive from variational principles. The action is discretized using…

Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…

We propose and study conformal integrators for linearly damped stochastic Poisson systems. We analyse the qualitative and quantitative properties of these numerical integrators: preservation of dynamics of certain Casimir and Hamiltonian…

In this paper, we study the asymptotic behavior for multi-scale stochastic differential equations driven by L\'evy processes. The optimal strong convergence order 1/2 is obtained by studying the regularity estimates for the solution of…

The spatial discretization of the magnetic vector potential formulation of magnetoquasistatic field problems results in an infinitely stiff differential-algebraic equation system. It is transformed into a finitely stiff ordinary…

Numerical methods that preserves geometric invariants of the system such as energy, momentum and symplectic form, are called geometric integrators. These include variational integrators as an important subclass of geometric integrators. The…

We consider a Stochastic Differential Equation driven by a L\'evy process whose L\'evy measure satisfy a tempered stable domination. We study how a perturbation of the coefficients reflects on the density of the solution. We quantify the…

Additive processes are obtained from L\'{e}vy ones by relaxing the condition of stationary increments, hence they are spatially (but not temporally) homogeneous. By analogy with the case of time-homogeneous Markov processes, one can define…

This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to…

Stochastic differential equations (SDE) often exhibit large random transitions. This property, which we denote as pathwise stiffness, causes transient bursts of stiffness which limit the allowed step size for common fixed time step explicit…

We develop efficient numerical integration methods for computing an integral whose integrand is a product of a smooth function and the Gaussian function with a small standard deviation. Traditional numerical integration methods applied to…

In this paper, we establish the optimal convergence result of a second order exponential-type integrator from (136, Numer. Math., 2017) for solving the KdV equation under rough initial data. The scheme is explicit and efficient to…

A general way to construct ladder models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. It is shown that corresponding to these SU(2) symmetric…

We present a method for efficient differentiable simulation of articulated bodies. This enables integration of articulated body dynamics into deep learning frameworks, and gradient-based optimization of neural networks that operate on…

The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…

Discrete Hamiltonian variational integrators are derived from Type II and Type III generating functions for symplectic maps, and in this paper we establish a variational error analysis result that relates the order of accuracy of the…

In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method first performs the spatial discretization of the model…