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We explore higher-dimensional generalizations of the Runge-Kutta-Wentzel-Kramers-Brillouin method for integrating coupled systems of first-order ordinary differential equations with highly oscillatory solutions. Such methods could improve…
Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by…
The shooting and finite-difference method are both numeric methods that approximate the solution of a BVP to a given accuracy. In this report both methods were implemented in Matlab and compared to each other on a BVP found in the context…
We propose in this paper a proximal and contraction method for solving a convex mixed variational inequality problem in a real Hilbert space. To accelerate the convergence of our proposed method, we incorporate an inertial extrapolation…
The main aim of this paper is to further develop a multiple-correction method formulated in a previous work~\cite{CXY}. As its applications, we find a kind of hybrid-type finite continued fraction approximations in two cases of Landau…
Recent dispersive techniques developed by us are applied to discuss three problems: 1. A long standing discrepan-cy between the measurements of $R(s)$ for $\sqrt{s} = (5\div 7.5)GeV$ by Crystal Ball and MARK I has been analyzed and its…
A system of equations resulting from an approximation of the equation of motion of Green functions for correlated electron systems is usually solved using Matsubara technique. In this work we propose an alternative method which works…
This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that…
We present a numerical method for convergence acceleration for multifidelity models of parameterized ordinary differential equations. The hierarchy of models is defined as trajectories computed using different timesteps in a time…
To obtain new types of exact travelling wave solutions to nonlinear partial differential equations, a number of approximate methods are known in the literature. In this study, we extend the class of auxiliary equations of Fibonnacci&Lucas…
We use the perturbation method to approximately solve subdiffusion-reaction equations. Within this method we obtain the solutions of the zeroth and the first order. The comparison our analytical solutions with the numerical results shown…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
The differential equation-based image restoration approach aims to establish learnable trajectories connecting high-quality images to a tractable distribution, e.g., low-quality images or a Gaussian distribution. In this paper, we…
This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and…
P-value functions are modern statistical tools that unify effect estimation and hypothesis testing and can provide alternative point and interval estimates compared to standard meta-analysis methods, using any of the many $p$-value…
Phase diversity is a widefield aberration correction method that uses multiple images to estimate the phase aberration at the pupil plane of an imaging system by solving an optimization problem. This estimated aberration can then be used to…
We propose a new approach to perform the boosted difference of convex functions algorithm (BDCA) on non-smooth and non-convex problems involving the difference of convex (DC) functions. The recently proposed BDCA uses an extrapolation step…
We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, termed variational boosting, iteratively refines an existing variational approximation…
The method of sub-iteration, which was previously applied to the higher-order coupled cluster amplitude equations, is extended to the case of the coupled cluster $\Lambda$ equations. The sub-iteration procedure for the $\Lambda$ equations…
Approximate solutions of the Fisher equation obtained by different splitting methods are investigated. The error of this nonlinear problem is analyzed. The order of different splitting methods coupled with numerical methods of different…