https://www.banglajol.info/index.php/GANIT/issue/feed GANIT: Journal of Bangladesh Mathematical Society 2020-08-12T15:29:33+00:00 Associate Editor ganit.bms@gmail.com Open Journal Systems <p>The official journal of the Bangladesh Mathematical Society. Full text articles available.</p> https://www.banglajol.info/index.php/GANIT/article/view/48191 Mathematical Model Applied to Monitoring the Glucose-Insulin Interaction inside the Body of Diabetes Patients 2020-07-20T20:34:49+00:00 Sonia Akter mhabiswas@yahoo.com Md Sirajul Islam mhabiswas@yahoo.com Md Haider Ali Biswas mhabiswas@yahoo.com Sajib Mandal mhabiswas@yahoo.com <p>The incidence and prevalence of diabetes are increasing all over the world and complication of diabetes constitutes a burden for the individuals and whole society. In this paper, we propose a mathematical model for monitoring glucose-insulin regulatory system in the human body. The non-linear cases are considered, and the model is analysed by using Lyapunov’s method. The mathematical model, discussed the critical situation of the diabetes patients as well as for normal person are analysed for stability. The numerical approximation is used to verify the analytical results and the obtained solutions represent the complex situation of diabetes patients.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 40 (2020) 1-12</p> 2020-07-14T00:00:00+00:00 ##submission.copyrightStatement## https://www.banglajol.info/index.php/GANIT/article/view/48192 A Comparative Study between Implicit and Crank-Nicolson Finite Difference Method for Option Pricing 2020-07-20T20:34:50+00:00 Tanmoy Kumar Debnath tanmoymathdu@gmail.com ABM Shahadat Hossain tanmoymathdu@gmail.com <p>In this paper, we have applied the finite difference methods (FDMs) for the valuation of European put option (EPO). We have mainly focused the application of Implicit finite difference method (IFDM) and Crank-Nicolson finite difference method (CNFDM) for option pricing. Both these techniques are used to discretized Black-Scholes (BS) partial differential equation (PDE). We have also compared the convergence of the IFDM and CNFDM to the analytic BS price of the option. This turns out a conclusion that both these techniques are fairly fruitful and excellent for option pricing.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 40 (2020) 13-27</p> 2020-07-14T00:00:00+00:00 ##submission.copyrightStatement## https://www.banglajol.info/index.php/GANIT/article/view/48193 Global Spectral Collocation Method with Fourier Transform to Solve Differential Equations 2020-07-20T20:34:52+00:00 Sayeda Irin Akter kamrujjaman@du.ac.bd Md Shahriar Mahmud kamrujjaman@du.ac.bd - Md Kamrujjaman kamrujjaman@du.ac.bd Hazrat Ali kamrujjaman@du.ac.bd <p>Numerical analysis is the area of mathematics that creates, analyzes, and implements algorithms for solving numerically the problems from real-world applications of algebra, geometry, and calculus, and they involve variables which vary continuously. Till now, numerous numerical methods have been introduced. Spectral method is one of those techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, potentially involving the use of the Fast Fourier Transform (FFT). This study presents some of the fundamental ideas of spectral method. Orthogonal basis are used to establish computational algorithm. The accuracy and efficiency of proposed model are discussed. This manuscript estimates for the error between the exact and approximated discrete solutions. This paper shows that, grid points for polynomial spectral methods should lie approximately in a minimal energy configuration associated with inverse linear repulsion between points. The wave equation, linear and non-linear boundary value problems are solved using spectral method on the platform of MATLAB language.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 40 (2020) 28-42</p> 2020-07-14T00:00:00+00:00 ##submission.copyrightStatement## https://www.banglajol.info/index.php/GANIT/article/view/48194 On the Convergence of Newton-like Method for Variational Inclusions under Pseudo-Lipschitz Mapping 2020-07-20T20:34:53+00:00 Mst Zamilla Khaton harun_math@ru.ac.bd MH Rashid harun_math@ru.ac.bd MI Hossain harun_math@ru.ac.bd <p>In the present paper, we study a Newton-like method for solving the variational inclusion defined by the sums of a Frechet differentiable function, divided difference admissible function and a set-valued mapping with closed graph. Under some suitable assumptions on the Frechet derivative of the differentiable function and divided difference admissible function, we establish the existence of any sequence generated by the Newton-like method and prove that the sequence generated by this method converges linearly and superlinearly to a solution of the variational inclusion. Specifically, when the Frechet derivative of the differentiable function is continuous, Lipschitz continuous, divided difference admissible function admits first order divided di_erence and the setvalued mapping is pseudo-Lipschitz continuous, we show the linear and superlinear convergence of the method.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 40 (2020) 43-53</p> 2020-07-14T00:00:00+00:00 ##submission.copyrightStatement## https://www.banglajol.info/index.php/GANIT/article/view/48195 Existence of Positive Solution for a Nonlinear Weighted Bi-Harmonic System of Elliptic Partial Differential Equations via Fixed-Point Argument 2020-07-20T20:34:54+00:00 - Md Asaduzzamana masad_iu_math@yahoo.com Md Zulfikar Ali masad_iu_math@yahoo.com <p>In this paper, we establish an existence criterion of positive solution for a nonlinear weighted bi-harmonic system of elliptic partial differential equations in the unit ball in N<sup>n</sup> ( dimensionaleuclideanspace) The analysis of this paper is based on a topological method (a fixed-point argument). Initially, we establish a priori solution estimates, and then use a fixed-point theorem for deducing the existence of positive solutions. Finally, we prove a non-existence criterion as the complement of existence criterion.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 40 (2020) 54-70</p> 2020-07-14T00:00:00+00:00 ##submission.copyrightStatement## https://www.banglajol.info/index.php/GANIT/article/view/48196 An Algorithmic Procedure for Finding Nash Equilibrium 2020-08-12T15:29:33+00:00 HK Das hkdas_math@du.ac.bd T Saha hkdas_math@du.ac.bd <p>This paper proposes a heuristic algorithm for the computation of Nash equilibrium of a bi-matrix game, which extends the idea of a single payoff matrix of two-person zero-sum game problems. As for auxiliary but making the comparison, we also introduce here the well-known definition of Nash equilibrium and a mathematical construction via a set-valued map for finding the Nash equilibrium and illustrates them. An important feature of our algorithm is that it finds a perfect equilibrium when at the start of all actions are played. Furthermore, we can find all Nash equilibria of repeated use of this algorithm. It is found from our illustrative examples and extensive experiment on the current phenomenon that some games have a single Nash equilibrium, some possess no Nash equilibrium, and others had many Nash equilibria. These suggest that our proposed algorithm is capable of solving all types of problems. Finally, we explore the economic behaviour of game theory and its social implications to draw a conclusion stating the privilege of our algorithm.</p> <p>GANIT <em>J. Bangladesh Math. Soc.</em>Vol. 40 (2020) 71-85</p> 2020-08-04T00:00:00+00:00 ##submission.copyrightStatement##