Numerical Analysis of Least-Squares Group Finite Element Method for Coupled Burgers' Problem

In this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved. The theoretical results show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the efficiency of the proposed method that are solved through implementation in MATLAB R2018a.

Impact of Approximate Implementation manner in Klobuchar Model

This paper focuses on the approximations that John A. Klobuchar made in mid 70s in his famous algorithm of ionospheric correction model for single frequency GPS receiver. At that time Klobuchar used a system of fixed geomagnetic north pole coordinates which are not accurate nowadays according to the International Geomagnetic Reference Field and to the World Magnetic Model because the geomagnetic poles move slowly. In addition, Klobuchar had to do other trigonometry simplifications in his implementation to avoid sophisticated computations. In order to evaluate this approximate implementation in a single frequency GPS receiver, ionospheric time and range delay are estimated on the entire day of January 1st 2010, using a different implementation in MATLAB. The required GPS data is obtained from recorded RINEX files at UDMC near DAMASCUS, SYRIA. In this comparative study, we reformulated the standard equations of Klobuchar model and examined the influence of its approximations on the ionospheric range delay and found a non- negligible bias in order of ten centimeters, whereas the influence of the movement of the geomagnetic poles was in order of few centimeters.

Fractional Derivatives Applied to Epidemiology

We seek investigate the use of fractional derivatives, both analytically and through simulations. We derivate some models and perform investigations about them, discussing difficulties and differences between classic and fractional models. Also, we analyzed the COVID-19 pandemic using a fractional epidemiological SIR model and performed a numerical analysis using finite differences and implementation in MATLAB.

MODIFICATION OF THE MINIMAL BERGMAN MODEL OF THE "INSULIN-GLUCOSE" SYSTEM AND ITS IMPLEMENTATION IN MATLAB/SIMULINK

The article discusses a modification of Bergman's minimal mathematical model of the "insulin-glucose" system, which allows simulating controlled exogenous sources of glucose and insulin into the patient's blood on the model and investigating the dynamics of changes in their concentrations in normal conditions, in type I DM and type II DM. A modeling scheme is presented in graphic notations of the MatLab / Simulink computer mathematics system and a number of computational experiments on it are described to determine the type of glycemic profiles of glucose and insulin concentration in the patient's blood in the noted situations. The fundamental possibility of using model mappings in the MatLab/Simulink environment for the study and tuning of the loop for automatic regulation of the "insulin-glucose" balance in the patient's blood using a controlled insulin pump is demonstrated. It was also found that the modified minimal model can be customized for a specific patient with diabetes, which makes it possible to use it to solve the problems of individual prediction of the development of a diabetic disease in a specific patient. In addition, the described model makes it possible to recreate and virtually investigate various conditions and cases on it that affect the dynamics of insulin and glucose concentrations in the patient's blood, for example, when he performs physically stressed activities, in the presence of the effects of “aging” of insulin-producing cells in the pancreas. iron, etc.

Study of Different Alternatives for Dynamic Simulation of a Steam Generator Using MATLAB

This work presents the simulation of a steam generator or water-tube boiler through the implementation in MATLAB® for a proposed mathematical model. Mass and energy balances for the three main components of the boiler - the drum, the riser and down-comer tubes - are presented. Three alternative solutions to the ordinary differential equation (ODE) were studied, based on Runge–Kutta 4th order method, Heun’s method, and MATLAB function Ode45. The best results were obtained using MATLAB® function Ode45 based on the Runge–Kutta 4th Order Method. The error was less than 5% for the simulation of the steam pressure in the drum, the total volume of water in the boiler, and the mixture quality in relation to what was reported.

On Fast Jerk–, Acceleration– and Velocity–Restricted Motion Functions for Online Trajectory Generation

Finding fast motion functions to get from an initial state (distance, velocity, acceleration) to a final one has been of interest for decades. For a solution to be practically relevant, restrictions on jerk, acceleration and velocity have to be taken into account. Such solutions use optimization algorithms or try to directly construct a motion function allowing online trajectory generation. In this contribution, we follow the latter strategy and present an approach which first deals with the situation where initial and final accelerations are 0, and then relates the general case as much as possible to this situation. This leads to a classification with just four major cases. A continuity argument guarantees full coverage of all situations which is not the case or is not clear for other available algorithms. We present several examples that show the variety of different situations and, thus, the complexity of the task. We also describe an implementation in MATLAB® and results from a huge number of test runs regarding accuracy and efficiency, thus demonstrating that the algorithm is suitable for online trajectory generation.

Approximate controllability of nonsimple elastic plate with memory

<p style='text-indent:20px;'>In this paper, we give some qualitative results on the behavior of a nonsimple elastic plate with memory corresponding to anti-plane shear deformations. First we describe briefly the equations of the considered plate and then we study the well-posedness of the resulting problem. Secondly, we perform the spectral analysis, in particular, we establish conditions on the physical constants of the plate to guarantee the simplicity and the monotonicity of the roots of the characteristic equation. The spectral results are used to prove the exponential stability of the solutions at an optimal decay rate given by the physical constants. Then we present an approximate controllability result of the considered control problem. Finally, we give some numerical experiments based on the spectral method developed with implementation in MATLAB for one and two-dimensional problems.</p>