Fractional Riccati equation to model the dynamics of COVID-19 coronovirus infection

The article proposes a mathematical model based on the fractional Riccati equation to describe the dynamics of COVID-19 coronavirus infection in the Republic of Uzbekistan and the Russian Federation. The model fractional Riccati equation is an equation with variable coefficients and a derivative of a fractional variable order of the Gerasimov-Caputo type. The solution to the model Riccati equation is given using the modified Newton method. The obtained model curves are compared with the experimental data of COVID-19 coronavirus infection in the Republic of Uzbekistan and the Russian Federation. It is shown that with a suitable choice of parameters in the mathematical model, the calculated curves give results close to real experimental data.

MN-PGSOR Method for Solving Nonlinear Systems with Block Two-by-Two Complex Symmetric Jacobian Matrices

For solving the large sparse linear systems with 2 × 2 block structure, the generalized successive overrelaxation (GSOR) iteration method is an efficient iteration method. Based on the GSOR method, the PGSOR method introduces a preconditioned matrix with a new parameter for the coefficient matrix which can enhance the efficiency. To solve the nonlinear systems in which the Jacobian matrices are complex and symmetric with the block two-by-two form, we try to use the PGSOR method as an inner iteration, with the help of the modified Newton method as an efficient outer iteration method. This new method is called the modified Newton-PGSOR (MN-PGSOR) method. Local convergence properties of the MN-PGSOR are analyzed under the Hölder condition. Finally, we give the comparison of our new method with some previous methods in the numerical results. The MN-PGSOR method is superior in both iteration steps and computing time.

NUMERICAL ITERATIVE METHOD OF OPEN METHODS WITH CONVERGE CUBICALLY FOR ESTIMATING NONLINEAR APPLICATION EQUATIONS

Finding the single root of nonlinear equations is a classical problem that arises in a practical application in Engineering, Physics, Chemistry, Biosciences, etc. For this purpose, this study traces the development of a novel numerical iterative method of an open method for solving nonlinear algebraic and transcendental application equations. The proposed numerical technique has been founded from Secant Method and Newton Raphson Method, and the proposed method is compared with the Modified Newton Method and Variant Newton Method. From the results, it is pragmatic that the developed numerical iterative method is improving iteration number and accuracy with the assessment of the existing cubic method for estimating a single root nonlinear application equation.

GPS Sparse Multipath Signal Estimation Based on Compressive Sensing

A GPS sparse multipath signal estimation method based on compressive sensing is proposed. A new 0 norm approximation function is designed, and the parameter of the approximate function is gradually reduced to realize the approximation of 0 norm. The sparse signal is reconstructed by a modified Newton method. The reconstruction performance of the proposed algorithm is better than several commonly reconstruction algorithms at different sparse numbers and noise intensities. The GPS sparse multipath signal model is established, and the sparse multipath signal is estimated by the proposed reconstruction algorithm in this paper. Compared with several commonly used estimation methods, the estimation error of the proposed method is lower.

Two new effective iteration methods for nonlinear systems with complex symmetric Jacobian matrices

In this paper, we mainly discuss the iterative methods for solving nonlinear systems with complex symmetric Jacobian matrices. By applying an FPAE iteration (a fixed-point iteration adding asymptotical error) as the inner iteration of the Newton method and modified Newton method, we get the so–called Newton-FPAE method and modified Newton-FPAE method. The local and semi-local convergence properties under Lipschitz condition are analyzed. Finally, some numerical examples are given to expound the feasibility and validity of the two new methods by comparing them with some other iterative methods.

Optimal control of spacecraft motion in the vicinity of Eros 433 asteroid

The article describes an algorithm for optimizing controlled motion of a spacecraft equipped with low-thrust electric propulsion engines maneuvering in the vicinity of an object with an irregular gravitational field (asteroid Eros 433). A mathematical model of the object’s gravitational potential and a model of spacecraft motion are presented. The Pontryagin maximum principle is used to get the time-optimal control program. The formulated boundary value problem is solved numerically by the modified Newton method. The described algorithm can be used to solve similar problems of low-thrust flight dynamics in the vicinity of objects with irregular gravitational fields.