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We consider a higher-order Milstein scheme for stochastic partial differential equations with trace class noise which fulfill a certain commutativity condition. A novel technique to generally improve the order of convergence of Taylor…
The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schr\"odinger-type equations and systems with a weak nonlinearity. To make a temporal step of the compact implicit scheme we…
We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…
We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
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.…
The stochastic Cahn-Hilliard equation driven by a fractional Brownian sheet provides a more accurate model for correlated space-time random perturbations. This study delves into two key aspects: first, it rigorously examines the regularity…
An innovative numerical technique is presented to adjust the inflow to a supply chain in order to achieve a desired outflow, reducing the costs of inventory, or the goods timing in warehouses. The supply chain is modelled by a conservation…
This paper serves to treat boundary conditions numerically with high order accuracy in order to match the two-stage fourth-order finite volume schemes for hyperbolic problems developed in [{\em J. Li and Z. Du, A two-stage fourth order…
Analyte response is convoluted with instrument response in time resolved fluorescence data. Decoding the desired analyte information from the measurement usually requires iterative numerical convolutions. Here in, we show that time resolved…
We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. The…
We are concerned with the numerical solution of a class integro-differential equations, known as Neural Field Equations, which describe the large-scale dynamics of spatially structured networks of neurons. These equations have many…
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
Quantum computers are believed to have the ability to process huge data sizes which can be seen in machine learning applications. In these applications, the data in general is classical. Therefore, to process them on a quantum computer,…
In this paper, we study the numerical schemes for the two-dimensional Fokker-Planck equation governing the probability density function of the tempered fractional Brownian motion. The main challenges of the numerical schemes come from the…
In general Evolutionary Computation (EC) includes a number of optimization methods inspired by biological mechanisms of evolution. The methods catalogued in this area use the Darwinian principles of life evolution to produce algorithms that…
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
Two numerical methods with graded temporal grids are analyzed for fractional evolution equations. One is a low-order discontinuous Galerkin (DG) discretization in the case of fractional order $0<\alpha<1$, and the other one is a low-order…
In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic…