Second order parameter-uniform convergence for a finite difference method for a singularly perturbed linear reaction-diffusion system

A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These singular perturbation parameters are assumed to be distinct. The components of the solution exhibit overlapping layers. Shishkin piecewise-uniform meshes are introduced, which are used in conjunction with a classical finite difference discretisation, to construct a numerical method for solving this problem. It is proved that the numerical approximations obtained with this method is essentially second order convergent uniformly with respect to all of the parameters

A parameter uniform fitted mesh method for a weakly coupled system of two singularly perturbed convection-diffusion equations

In this paper, a boundary value problem for a singularly perturbed linear system of two second order ordinary differential equations of convection- diffusion type is considered on the interval [0, 1]. The components of the solution of this system exhibit boundary layers at 0. A numerical method composed of an upwind finite difference scheme applied on a piecewise uniform Shishkin mesh is suggested to solve the problem. The method is proved to be first order convergent in the maximum norm uniformly in the perturbation parameters. Numerical examples are provided in support of the theory

Nonlinear system identification and control using state transition algorithm

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 optimization problem is considered as a state, and the updating of a solution equates to a state transition, which makes it easy to understand and convenient to implement. First, the STA is applied to identify the optimal parameters of the estimated system with previously known structure. With the accurate estimated model, an off-line PID controller is then designed optimally by using the STA as well. Experimental results have demonstrated the validity of the methodology, and comparisons to STA with other optimization algorithms have testified that STA is a promising alternative method for system identification and control due to its stronger search ability, faster convergence rate and more stable performance.Comment: 20 pages, 18 figure

Food concepts expounded in Sangam texts

The human quest for food led to their cultural development. This is called "Undi Muthatrae Lokagu". The food culture found in Sangam literature is a testimony to the cultural development of the Tamils. The reference to "food" in literature is surprising. "Food is water that touches the ground." This understanding is very, very subtle and very surprising. Even in the Sangam literature, the Tamils had an understanding that the component of every food depends on land and water. Moreover, eating was considered as a social activity rather than a physical necessity. The social character of food is indicated by the importance given to the serving of food to the guests in those days and the importance of food in family and local events. Moreover, giving man food for survival was seen as highly admirable. The proverb says, "Those who feed are those who give life."

The Widow's Reincarnation bound in Revolutionary Poetic Writing

When Bharathiar sings about women and their problems, he sings that women should fight for the freedom of the country and fight for their freedom. He has also elevated women to motherhood as a symbol of power. But Bharathidasan looks closely at the problems of women's lives and analyses and sings the social problems of women, such as widowhood, superstition, child marriage, etc. Bharathidasan tried to eliminate the disadvantages faced by women in society. In general, he warns men that he does not want to justify everything that men do in society. The situation of women in our country is very deplorable. From the foot to the top, the whole body should be corrected. It must be said that the slavery of women is due to the superstitious practices of our country. Pavendar Bharathidasan can be regarded as someone who worked hard to change the situation of women by associating himself with Periyar's rationality and ideas. While women's society cannot be completely reformed, there is a sense of reform among semi-educated women. The remarriage of the widow can be specifically pointed out. Through his works, it can be said that Pavendar Bharathidasan was the one who sowed the seeds of widow remarriage

Principles of Siva in Thirumanthiram

Thirumoolar has the principle that 'There is One Race and One God'. He has accepted Lord Shiva as the great deity in his Thirumanthiram. When we say the greatness of Shiva, it is said that 'Shiva is the one who directs the world just as life fits into the body and directs the body', therefore, Shiva is the life of the world. He who has many worlds as a body, he is the one God of all the worlds. Thirumanthiram describes this as "One who has seen it and a Deity for the World". Thirumanthiram has used many mythological stories here and there to make people aware of many rare truths. Among them, this article is to examine the nature of Eesan in the Thirumanthiram, which depicts the deeds and grace of Lord Shiva

Characterization of the female protagonist in Kurunthogai

Tamil poets have created, named, categorized, summarized and preserved dialects based on dialects in order to preserve the language they speak. Before exploring the importance of numbers in language it is necessary to know the design of grammatical literature. It is possible that the Sanskrit poets called the text grammar of the words when they recorded the language, they created in the journals so that it would be known to the world, and the textual literature of the world empirical biographies based on his quote characters. The words created for measurements such as size and mass are the primary letters of the words and the reasons for giving a special place to measurements in Tamil are explained. In order to give Tamil a lofty place in the world languages ​​in are the numbers to indicate the of an action, the time of action, and the number of soldiers involved in the war