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Noise in initial conditions from measurement errors can create unwanted oscillations which propagate in numerical solutions. We present a technique of prohibiting such oscillation errors when solving initial-boundary-value problems of…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
By transforming identification and control for nonlinear system into optimization problems, a novel optimization method named state transition algorithm (STA) is introduced to solve the problems. In the proposed STA, a solution to a…
The purpose of the paper is twofold. Firstly, we want to present a Meta Theorem to show the existence of a martingale solution for coupled systems of non-linear stochastic differential equations. The idea is first to split the system by…
In this paper we propose a modified Lie-type spectral splitting approximation where the external potential is of quadratic type. It is proved that we can approximate the solution to a one-dimensional nonlinear Schroedinger equation by…
Mesoscopic models in the reaction-diffusion framework have gained recognition as a viable approach to describing chemical processes in cell biology. The resulting computational problem is a continuous-time Markov chain on a discrete and…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
Differential Riccati equations (DREs) are semilinear matrix- or operator-valued differential equations with quadratic non-linearities. They arise in many different areas, and are particularly important in optimal control of linear quadratic…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of…
The dynamics of cross-diffusion models leads to a high computational complexity for implicit difference schemes, turning them unsuitable for tasks that require results in real-time. We propose the use of two operator splitting schemes for…
In this paper we consider a system of three fractional differential equations describing a nonlinear reaction. Our analysis includes both analytical technique and numerical simulation. This allows us to control the efficiency of the…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
This work proposes a research problem of finding sparse solution of undetermined Linear system with some applications. Two approaches how to solve the compressive sensing problem: using l_1 approach , the l_q approach with 0 < q < 1.…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
A system of equations of the reaction-diffusion type is studied in the framework of both the direct and the inverse prolongation structure. We find that this system allows an incomplete prolongation Lie algebra, which is used to find the…