ஜர்னல் ஆஃப் அப்ளைடு & கம்ப்யூட்டேஷனல் கணிதம்

Sugarcane is a main economic crop to the farmers. The farmers, the people and the factories depend on this crop. Farmers who are cultivating the sugarcane have to send to their product to the nearest factories. Some vehicles are utilized for transporting the sugarcane to the factory. The vehicles are lorries, bullock carts or tractors. If the cost of transportation of sugarcane, sent to the factory is minimum, then the total processing cost will also be minimized. In this paper, the idea of minimum transportation cost is discussed using Linear Programming Problems and the mode of transportation between the field and the factory. The possibility of loss due to accident is also discussed in order to get ready for the sudden loss of the product.

In this paper, the differential transformation method is modified to be easily employed to solve wide kinds of nonlinear initial-value problems. In this approach, the nonlinear term is replaced by its Adomian polynomials for the index k, and hence the dependent variable components are replaced in the recurrence relation by their corresponding differential transform components of the same index. Thus the nonlinear initial-value problem can be easily solved with less computational effort. New theorems for product and integrals of nonlinear functions are introduced. In order to show the power and effectiveness of the present modified method and to illustrate the pertinent features of related theorems, several numerical examples with different types of nonlinearities are considered.

In this article, a new application of Differential Transformation Method (DTM) is presented to find exact and approximate solutions of the heat equation in the cast-mould heterogeneous domain. It is indicated that the solutions obtained by the two dimensional (DTM) are reliable, useful and effective method for decouple partial differential equations. Exact solutions can also be obtained from the known forms of the series solutions.

The main objective of the present paper is to achieve a modified numerical method for investigating the vibration characteristics of the stepped thickness plate with many types of boundary conditions surrounding certain number of panels. The presented technique relies on dividing the entire plate into several regions of uniform thickness separated by sudden steps. Each region is divided to number of strips which are assembled and solved numerically by the Finite Strip-Transition Matrix method FSTM. A convenient basic function is applied to reduce the partial differential equation of motion of plate inside a single region into an ordinary differential one. Step continuity conditions are applied to achieve the final solution of plate. Regional rigidities of plates and mass per unit area are changed due to the change of plate thickness from a region to another. Consequently, new straining actions are occurred and then compatibility conditions become necessary to modify the nodal vector at each step. Various types of restrained boundary conditions against rotation are included in the present paper. The validity of present method is checked and the accuracy of the results is compared with those available in literature showing a good agreement.

A new conjugate gradient method is proposed for solving the linear ill-posed problem and the application to the identification of the multi-source dynamic loads on a surface of simply supported plate. The algorithm considered here is detailedly given and proved that the computational costs for the present method are nearly the same as the common conjugate gradient method, but the number of iteration steps is even less. Finally, the performances of numerical simulations are given, and verify the favorable theoretical properties of the present method.