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Search Results: 1 - 10 of 6490 matches for " Md. Shafiqul Islam "
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 Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.29147 Abstract: The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the approximate solutions of 2nd order boundary value problems. Here the Bernoulli polynomials over the interval [0,1] are chosen as trial functions so that care has been taken to satisfy the corresponding homogeneous form of the Dirichlet boundary conditions in the Galerkin weighted residual method. In addition to that the given differential equation over arbitrary finite domain [a,b] and the boundary conditions are converted into its equivalent form over the interval [0,1]. All the formulas are verified by considering numerical examples. The approximate solutions are compared with the exact solutions, and also with the solutions of the existing methods. A reliable good accuracy is obtained in all cases.
 American Journal of Computational Mathematics (AJCM) , 2019, DOI: 10.4236/ajcm.2019.91001 Abstract: The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.
 Communications and Network (CN) , 2013, DOI: 10.4236/cn.2013.53B2048 Abstract: The spot-diffusing technique provides better performance compared to conventional diffuse system for indoor optical-wireless communication (OWC) system. In this paper, the performance of an OW spot-diffusing communication system using Neuro-Fuzzy (NF) adaptive multi-beam transmitter configuration has been proposed. The multi-beam transmitter generates multiple spots pointed in different directions, hence, forming a matrix of diffusing spots based on position of the receiver and receiver mobility. Regardless of the position of the transmitter and receiver, NF controller target the spots adaptively at the best locations and allocates optimal power to the spots and beam angle are adapted in order to achieve better signal-to-noise plus interference ratio (SNIR). Maximum ratio combining (MRC) is used in the imaging receiver. The proposed OW spot-diffusing communication system is compared with other spot-beam diffusion methods proposed in literature. Performance evaluation revels that the proposed NF based OW spot-diffusing communication system outperforms other spot-beam diffusion methods.
 Computer Science , 2013, DOI: 10.3329/jsr.v2i2.4483 Abstract: In this paper, Bernstein piecewise polynomials are used to solve the integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin method, the Bernstein polynomials are used as the approximation of basis functions. Examples are considered to verify the effectiveness of the proposed derivations, and the numerical solutions guarantee the desired accuracy.