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In this research work, Galerkin and collocation methods have been introduced for approximating the solution of FIE of 2nd kind using LH (product of Laguerre and Hermite) polynomials which are considered as basis functions. Also, a comparison has been done between the solutions of Galerkin and collocation method with the exact solution. Both of these methods show the outcome in terms of the approximate polynomial which is a linear combination of basis functions. Results reveal that performance of collocation method is better than Galerkin method. Moreover, five different polynomials such as Legendre, Laguerre, Hermite, Chebyshev 1st kind and Bernstein are also considered as a basis functions. And it is found that all these approximate solutions converge to same polynomial solution and then a comparison has been made with the exact solution. In addition, five different set of collocation points are also being considered and then the approximate results are compared with the exact analytical solution. It is observed that collocation method performed well compared to Galerkin method. GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 11-25

Multi-objective simplex algorithm computes all efficient extreme points of a multi-objective linear programming (MOLP) problem. For MOLP problem with large number of efficient extreme points, a filtering technique is necessary to present a small representative part of efficient extreme points. For this, we propose a filtering technique among efficient extreme points. In modern agriculture, we have to consider series of conflicting optimization criteria. For this reason, optimal cropping pattern, that is, allocation of land to various crops by making use of limited resources has become major challenges to get optimum return. To overcome this challenge, we illustrate the application of MOLP through a real life oriented problem of agricultural sector of Bangladesh. We also solve this problem by a self developed computer software which is based on multi-objective simplex algorithm and our proposed filtering technique. Dhaka Univ. J. Sci. 64(2): 147-152, 2016 (July)

Formulation of LPs and IPs is a technique to convert real life decision problems into a mathematical model. This model consists of a linear objective function and a set of linear constraints expressed in the form of a system of equations or inequalities. In this paper, we present formulation from real life problem as an art. We discuss formulation through real life example and solve them using computer techniques AMPL and LINDO. DOI: http://dx.doi.org/10.3329/dujs.v61i2.17068 Dhaka Univ. J. Sci. 61(2): 185-191, 2013 (July)