Related papers: An efficient step size selection for ODE codes
We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of…
We introduce an efficient first-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this efficiency through not solving the PDE or its linearisation on each iteration of the optimization…
Computational efficiency demands discretised, hierarchically organised, and individually adaptive time-step sizes (known as the block-step scheme) for the time integration of N-body models. However, most existing N-body codes adapt…
In this article, firstly we develop a method for a type of difference equations, applicable to solve approximately a class of first order ordinary differential equation systems. In a second step, we apply the results obtained to solve a…
Recent results in homotopy and solution paths demonstrate that certain well-designed greedy algorithms, with a range of values of the algorithmic parameter, can provide solution paths to a sequence of convex optimization problems. On the…
Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…
We show that accelerated gradient descent, averaged gradient descent and the heavy-ball method for non-strongly-convex problems may be reformulated as constant parameter second-order difference equation algorithms, where stability of the…
In this paper, we deal with multiobjective composite optimization problems, where each objective function is a combination of smooth and possibly non-smooth functions. We first propose a parameter-dependent conditional gradient method to…
An efficient method is described to handle mesh indexes in multidimensional problems like numerical integration of partial differential equations, lattice model simulations, and determination of atomic neighbor lists. By creating an…
We implement an adaptive step size method for the Hybrid Monte Carlo a lgorithm. The adaptive step size is given by solving a symmetric error equation. An integr ator with such an adaptive step size is reversible. Although we observe…
ODE solvers with randomly sampled timestep sizes appear in the context of chaotic dynamical systems, differential equations with low regularity, and, implicitly, in stochastic optimisation. In this work, we propose and study the stochastic…
We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime. Focusing on discontinuous…
In the paper an efficient semi-analytical approach based on the method of steps and differential transformation is proposed for numerical approximation of solutions of retarded logistic models of delayed and neutral type, including models…
We consider stochastic approximation with block-coordinate stepsizes and propose adaptive stepsize rules that aim to minimize the expected distance from the next iterate to an (unknown) target point. These stepsize rules employ online…
In this paper, we consider effective discretization strategies and iterative solvers for nonlinear PDE-constrained optimization models for pattern evolution within biological processes. Upon a Sequential Quadratic Programming linearization…
This paper gives some theory and efficient design of binary block systematic codes capable of controlling the deletions of the symbol ``$0$'' (referred to as $0$-deletions) and/or the insertions of the symbol ``$0$'' (referred to as…
Gradient methods are experiencing a growth in methodological and theoretical developments owing to the challenges posed by optimization problems arising in data science. However, such gradient methods face diverging optimality gaps or…
Stiff ordinary differential equations (ODEs) are common in many science and engineering fields, but standard neural ODE approaches struggle to accurately learn these stiff systems, posing a significant barrier to widespread adoption of…
The concept of integration is generally applicable to automatic control of processes. As shown in this paper, integral controller performs efficient searches in the extensive prime sets, too. An inspiration by the simple analytic rules for…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…