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Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle…

First of all, this paper presents some improvements of DSMC method in the form of new schemes and approaches, that, for a wide class of problems, increase performance and reduce the demands on computer resources. The most important…

Magnetohydrodynamics (MHD) is a continuum level model for conducting fluids subject to external magnetic fields, e.g. plasmas and liquid metals. The efficient and robust solution of the MHD system poses many challenges due to it's…

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of…

We show that with a few modifications the Adomian's method for solving second order differential equations can be used to obtain the known results of the special functions of mathematical physics. The modifications are necessary in order to…

This note proposes a new reformulation of complex semidefinite programs (SDPs) as real SDPs. As an application, we present an economical reformulation of complex SDP relaxations of complex polynomial optimization problems as real SDPs and…

In the literatur there exist approximation methods for McKean-Vlasov stochastic differential equations which have a computational effort of order $3$. In this article we introduce full-history recursive multilevel Picard (MLP)…

A method to construct the exact solution of the PDE is presents, which combines the two kind methods(the nonlinear transformation and RQ(Reduction the PDE to a Quadrature problem) method).The nonlinear diffusion equation is chosen to…

A Weierstrass type projective Riccati equation expansion method is proposed by using the Weierstrass elliptic function solutions of the projective Riccati equations and the conversion formulas which transform the Weierstrass elliptic…

A formula to construct classic exact solutions to Tricomi partial differential equation. The steps to obtain this formula require only elementary resolution of a simple system of first order PDEs.

We propose a novel version of the dissipative Gross--Pitaevski equation and examine its properties. In contrast to previous proposals our approach, based on the metriplectic formulation of the dissipative system dynamics, conserves the…

This paper investigates a class of generalized mean-reflected McKean-Vlasov type backward stochastic differential equations (BSDEs). Our new framework combines a mean reflection constraint on the solution's expectation with a generalized…

In this paper, the aim is to develop a quantum counterpart to classical Markov decision processes (MDPs). Firstly, we provide a very general formulation of quantum MDPs with state and action spaces in the quantum domain, quantum…

This paper will be replaced later by a revised version.

This paper is a continuation of our recent work in [9].

A recent line of research has exploited pre-trained generative diffusion models as priors for solving Bayesian inverse problems. We contribute to this research direction by designing a sequential Monte Carlo method for linear-Gaussian…

In the previous work [2] (i.e., arXiv:2105.03385), we considered continuous solutions of an iterative equation involving the multiplication of iterates. In this paper, we continue to investigate this equation for differentiable solutions.…

In this paper we present a unified method for solving general polynomial equations of degree less than five.

In this note, two numerical methods of solving fractional differential equations (FDEs) are briefly described, namely predictor-corrector approach of Adams-Bashforth-Moulton type and multi-step generalized differential transform method…

We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of…