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Numerical Solutions of a Class of Second Order Boundary Value Problems on Using Bernoulli Polynomials  [PDF]
Md. Shafiqul Islam, Afroza Shirin
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.
Comparison of Classical Method, Extension Principle and α-Cuts and Interval Arithmetic Method in Solving System of Fuzzy Linear Equations  [PDF]
Sahidul Islam, Md. Saiduzzaman, Md. Shafiqul Islam, Abeda Sultana
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.
Effect of Salinity Stress on Growth and Yield of Forage Genotypes  [PDF]
Pijush Kanti Ghosh, Md. Shafiqul Islam, Sarder Safiqul Islam
Agricultural Sciences (AS) , 2021, DOI: 10.4236/as.2021.129061
Abstract: Salinity is the major limiting factor for forage productivity in southwestern coastal region of Bangladesh. Some introduced forage cultivars have been shown promising adaptability in saline conditions. The objective of this study was to assess the productivity and measure the agronomic characteristics of several introduced grass species with different created soil salinity levels. This study was conducted at the net house of Dr. Purnendu Gain Field Laboratory, Agrotechnology Discipline, and Khulna University during the period from December 2017 to February 2018. The experiment was laid out in a factorial randomized complete block design with seven replications. The experiment consisted of two factor viz. soil salinity levels (S1 = 0.48, S2 = 5.8, S3 = 7.9, S4 = 9.4, S5 = 15 d·Sm−1) and thirteen forage genotypes. Salinity levels and forage genotypes significantly (p < 0.05) influence all the growth parameters and biomass yield. The growth parameters and yield gradually decreased with the advance of soil salinity level. The tallest plant height (109.85 cm) was found in S1 at 90 DAS while the shortest plant (24.53 cm) was obtained in S5 at 90 DAS. Soil salinity had a significant difference (p < 0.001) on plant height at 90 DAS. The highest numbers of tillers (3.36) were found in S1, whereas the lowest (0.48) was in S5 at 75 DAS. Soil salinity had a significant difference (p < 0.001) on Number of tillers at 75 DAS. The highest biomass wt. (29.14 g) was found in S1, while the lowest biomass wt. (3.52 g) was obtained in S5 at 60 DAS. Soil salinity had a significant difference (p < 0.001) on biomass wt. at 60 DAS. The highest dry matter% (DM%) (21.24%) was found in S4, while the lowest DM (18.74%) was obtained in S1 at 60 DAS. Soil salinity had a significant difference (p < 0.001) on dry matter% (DM%) wt. at 90 DAS. The tallest plant height (81.93 cm) was found in Pakchong, while the shortest plant (20.13 cm) was obtained in Endropogan at 60DAS. Soil salinity had a significant difference (p < 0.001) on plant height at 60 DAS. The highest numbers of tillers (3.07) were also found in Napier-3, whereas the lowest (0.80) was in H. Jaumbo at 75 DAS (S1 + S2 + S3 + S4 + S5). Soil salinity had a significant difference (p < 0.001) on
Prematur e Ejaculation and Chronic Bacterial Prostatitis
Md Shafiqul Islam
Medicine Today , 2017, DOI: https://doi.org/10.3329/medtoday.v29i2.34621
Abstract: Premature ejaculation (PE) is regarded as the most common male sexual disorder. Previous studies reported that prostatic inflammation was highly prevalent in PE. However, the effect of antibiotic treatment of cases with PE and chronic prostatitis has not been extensively investigated. To examine the effect of antibiotic treatment in delaying ejaculation in patients with PE and chronic prostatitis. The study was carried out in my private chamber and at General Hospital N.Gong from June 2014 to December 2016. The study was performed with prior permission and the confidentiality was maintained. A total of 135 consecutive men attending of secondary premature ejaculation (SPE) were included in this study. Sequential microbiologic specimens were obtained from urine and prostatic fluids. Antibiotics were given for one month according to the results of their culture and sensitivity test. All patients were instructed to follow up in General Hospital N.Gong/Private chamber monthly for at least 4 months. At the end of the 4-month follow-up, another prostatic secretion analysis was performed. Based on expressed prostatic secretion culture and white blood cell (WBC) count, 84 (62.2%) were having chronic bacterial prostatitis. The remaining 51 (37.8%) patients had negative WBC count. Of the 84 patients with secondary premature ejaculation (SPE) and chronic bacterial prostatitis, 20 patients were left untreated and considered as a control group. All 64 patients with PE and chronic prostatitis continued the 1- month treatment duration. Following 1-month antibiotic treatment, all 64 patients with initially positive cultures had sterile final cultures (P < 0.05). Fifty one (79.68%) patients showed increases in their ejaculatory latency time and reported good control of their ejaculation and were considered treatment responsive. None of the control group patients experienced any improvement either in their prostatic infection condition or in their ejaculation time. The follow-up of treatment-responsive patients (N = 51) revealed no recurrence of PE with negative prostatic culture. Successful eradication of causative organisms in patients with PE and chronic prostatitis may lead to marked improvement in intravaginal ejaculatory latency time and ejaculatory control. Medicine Today 2017 Vol.29(2): 21-25
Numerical Analysis for Determination of Hydrodynamic Characteristics of a Gimbaled Thrust Vectoring Nozzle
Md Shafiqul Islam,Saad Islam
Journal of Bangladesh Academy of Sciences , 2017, DOI: https://doi.org/10.3329/jbas.v41i1.33505
Abstract: Gimbaled thrust vectoring nozzles are employed in Solid Rocket Motors (SRM) to account for the aspects of maneuverability of the flight vehicle. The flow field of such a solid pulsed rocket motor is explored numerically (from dome-closeout onward) by solving Reynolds-averaged Navier-Stokes equations with Menters Shear Stress Transport (SST) k - ? turbulence model using a Computational Fluid Dynamics (CFD) tool. Parametric studies are carried out to find out the thermochemical and hydrodynamic characteristics of the hot gas in the rocket motor nozzle. The performances of different supersonic and subsonic sections were studied in terms of the hydrodynamic aspects such as static pressure and Mach number distribution. It is observed that the tradeoff of implementing thrust vectoring mechanism amounts to an additional pressure loss of 10.06% in the rocket motor. Such analyses are specific to certain types of Short Range Ballistic Missiles (SRBM) having solid state propellant (primary stage) in radial boost, end burning pulsed configuration with exacting demands on maneuverability and control implied upon payload and mission criterion. Journal of Bangladesh Academy of Sciences, Vol. 41, No. 1, 69-84, 2017
Performance Analysis of Optical Wireless Communication System Employing Neuro-Fuzzy Based Spot-Diffusing Techniques  [PDF]
Shamim Al Mamun, M. Shamim Kaiser, Muhammad R Ahmed, Md. Shafiqul Islam, Md. Imdadul Islam
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.
Efficacy of Some Botanical Extracts on the Control of Late Blight Disease in Experimental Potato Field  [PDF]
Shafiqul Islam, Md. Abul Kalam Azad, Md. Rashidul Islam, Mst. Samia Sultana, Jesmin Ara Khatun, Md. Huzzatul Islam
Advances in Bioscience and Biotechnology (ABB) , 2021, DOI: 10.4236/abb.2021.1212027
Abstract: Late blight caused by Phytophthora infestans (Mont.) De Bary is the most devastating disease of potato. This study was carried out to evaluate the efficacy of ten botanical extracts against the late blight disease incidence and severity in experimental potato field at University of Rajshahi, Bangladesh during 2019-2020. Crude aqueous extract of leaves of Syzygium cumini, Psidium guajava, Eucalyptus globusus, Carica papaya and Lawsonia inermis; fruits of Terminalia bellirica, T. chebula and Piper nigrum; flower buds of Syzygium aromaticum and cloves of Allium sativum were used at 5% (w/v) concentration for evaluation. Out of ten botanicals, Syzygium cumini leaves extract was found most effective in controlling the late blight disease incidence and severity up to 66 DAS (days after sowing) and increased the potato yield by 71.29% compare to untreated control. The efficacy of Lawsonia inermis extract against late blight disease was found promising and increased the potato yield by 48.51%. Other four botanical extracts (Terminalia chebula, Piper nigrum, Syzygium aromaticum and Carica papaya) showed moderate efficacy against the incidence and severity of late blight disease, and increased 30% more potato yield compare to control. These results suggest that botanical extract of Syzygium cumini has a great potential as an alternative of chemical fungicides to control the late blight disease of potato in eco-friendly way.
Numerical Solutions of Fredholm Integral Equations Using Bernstein Polynomials
Afroza Shirin,Md. Shafiqul Islam
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.
Generalized Galerkin Finite Element Formulation for the Numerical Solutions Of Second Order Nonlinear Boundary Value Problems
Hazrat Ali,Md Shafiqul Islam
GANIT: Journal of Bangladesh Mathematical Society , 2017, DOI: https://doi.org/10.3329/ganit.v37i0.35733
Abstract: We use Galerkin finite element method (GFEM) to solve second order linear and nonlinear boundary value problems (BVPs). First we develop FEM formulation for a class of linear and nonlinear BVPs. Then we present convergence analysis of the method. Later, we give the solution of some nonlinear BVPs with Diritchlet, Neumann and Robin boundary conditions. All results are compared with the exact solution and sometimes with the results of the existing method to verify the convergence, stability and consistency of this method. The results are depicted graphically as well as in the tabular form. GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 147-159
Galerkin-Bernstein Approximations for the System of Third-Order Nonlinear Boundary Value Problems  [PDF]
Snigdha Dhar, Md. Shafiqul Islam
Journal of Applied Mathematics and Physics (JAMP) , 2024, DOI: 10.4236/jamp.2024.126127
Abstract: This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory.
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