Journal of Applied Mathematics and Computational Mechanics 

About: Journal of Applied Mathematics and Computational Mechanics is an academic journal published by The Publishing Office of Czestochowa University of Technology. The journal publishes majorly in the area(s): Computational mechanics & Finite element method. It has an ISSN identifier of 2299-9965. It is also open access. Over the lifetime, 483 publications have been published receiving 1495 citations.

Facility layout redesign for efficiency improvement and cost reduction

Abstract: In a competitive market the manufacturing companies have to produce cost effective products which can be realized by minimized production cost and higher effectiveness. The effective facility planning can significantly reduce the operational costs of companies. An adequate facility layout can result in the improvement of the performance of the production line. The Facility Layout Problem (FLP) is relating to location of objects (departments, workstations, machines, etc.) on a given site and the material flow between these objects. The goal of this study is to show the reasons, objectives and steps of a layout redesign process. The minimization of the workflow realized on the shop floor is an often applied an objective function during the layout redesign. Material flow efficiency is a commonly used term for the determination of the amount of workflow, which is the multiplication of material flow data and distance data. In this study, this mathematical method for workflow calculation is introduced. The described case study shows how the efficiency and reduced manufacturing cost of a real manufacturing system can be improved by re-layout design, while smaller floor space is needed for the production. MSC 2010: 91B32

Thermal performance of porous fins with temperature-dependent heat generation via the homotopy perturbation method and collocation method

Abstract: An analysis has been performed to study the problem of the thermal performance of a nonlinear problem of the porous fin with temperature-dependent internal heat generation. Highly accurate semi-analytical methods called the collocation method (CM) and the homotopy perturbation method (HPM) are introduced and then are used to obtain a nonlinear temperature distribution equation in a longitudinal porous fin. This study is performed using passage velocity from the Darcy’s model to formulate the heat transfer equation through porous media. The heat generation is assumed to be a function of temperature. The effects of the natural convection parameter Nc, internal heat generation εg, porosity Sh and generation number G parameter on the dimensionless temperature distribution are discussed. Also, numerical calculations called the fourth order Runge-Kutta method were carried out for the various parameters entering into the problem for validation. Results reveal that analytical approaches are very effective and convenient. Also it is found that these methods can achieve more suitable results compared to numerical methods.

Using Shehu integral transform to solve fractional order Caputo type initial value problems

Abstract: In the present research analysis, linear fractional order ordinary differential equations with some defined condition (s) have been solved under the Caputo differential operator having order α > 0 via the Shehu integral transform technique. In this regard, we have presented the proof of finding the Shehu transform for a classical nth order integral of a piecewise continuous with an exponential order function which leads towards devising a theorem to yield exact analytical solutions of the problems under investigation. Varying fractional types of problems are solved whose exact solutions can be compared with solutions obtained through existing transformation techniques including Laplace and Natural transforms. MSC 2010: 26A33, 34M03.

Dual-phase lag equation. Stability conditions of a numerical algorithm based on the explicit scheme of the finite difference method

Abstract: The dual-phase lag equation (DPLE) is considered. This equation belongs to the group of hyperbolic PDE, contains a second order time derivative and higher order mixed derivative in both time and space. From the engineer’s point of view, the DPLE results from the generalized form of the Fourier law. It is applied as a mathematical model of thermal processes proceeding in the micro-scale and also in the case of bio-heat transfer problem analysis. At the stage of numerical computations the different approximate methods of the PDE solving can be used. In this paper, the authors present the considerations concerning the stability conditions of the explicit scheme of finite difference method (FDM). The appropriate conditions have been found using the von Neumann analysis. In the final part of the paper, the results of testing computations are shown.

Linear logic in computer science

Abstract: Linear logic has many properties that make it suitable for application in various areas of computer science It is able to describe dynamic processes, non-determinism, parallelism on syntactic level In our paper we try to discuss resource oriented character of linear logic, its possibility to deal with such important resources for computer science as space (memory) and time Handling with resources takes place in deduction system of linear logic We show how special form of proofs, called designs, is constructed and we show the relationship between space and time in designs