A virus spread by mosquitoes called dengue fever affects millions of people each year and is a serious threat to world health. More than 140 nations are affected by the illness of dengue fever. Therefore, in this paper, a Susceptible-Infectious-Recovered (SIR) mathematical model for the host (human) and vector (dengue mosquitoes) has been presented to describe the transmission of dengue in Bangladesh. In the model the vector are related with two compartments that are susceptible and infective and host are related with three compartments that are susceptible, infective, and recovered. By these five compartments, five connected nonlinear ordinary differential equations (ODEs) are produced. As a result of non dimensionalization, a system of three nonlinear ODEs has been generated. The reproductive number and equilibrium points have been estimated for different cases. In order to compute the infection rate, data for infected human populations have been gathered from multiple health institutes in Bangladesh. MATLAB has been utilized to construct numerical simulations of different compartments in order to examine the impact of critical parameters on the disease’s propagation and to bolster the analytical findings. The simulated outcomes for susceptible, infected, and eliminated in graphical formats have been displayed. The paper’s main goal is to emphasize the uniqueness of computational analysis of the SIR mathematical model for the dengue fever.

Remittance is the tie that is sent to the country by earning money from abroad. In present Bangladesh, remittance is playing an important role in increasing reserves and revenue. For about two decades remittance has been contributing a huge portion of export earnings. Remittances have a significant impact on the budget of Bangladesh and also the budget depends a lot on remittances. So it is very crucial to know the future remittance to make an annual budget for upcoming year. This paper concentrates on choosing the appropriate smoothing constants for foreign remittances forecasting by Holt’s method. This method is very popular quantitative skilled in forecasting. The forecasting of this deftness depends on optimal smoothing constants. So, choosing an optimal smoothing constant is very important to minimize the error of forecasting. We have demonstrated the techniques by presenting actual remittances and also presented graphical comparisons between actual and forecasting remittances for the optimal smoothing constants.

There exist numerous numerical methods for solving the initial value problems of ordinary differential equations. The accuracy level and computational time are not the same for all of these methods. In this article, the Modified Euler method has been discussed for solving and finding the accurate solution of Ordinary Differential Equations using different step sizes. Approximate Results obtained by different step sizes are shown using the result analysis table. Some problems are solved by the proposed method then approximated results are shown graphically compare to the exact solution for a better understanding of the accuracy level of this method. Errors are estimated for each step and are represented graphically using Matlab Programming Language and MS Excel, which reveals that so much small step size gives better accuracy with less computational error. It is observed that this method is suitable for obtaining the accurate solution of ODEs when the taken step sizes are too much small.

Many different methods are applied and used in an attempt to solve higher order nonlinear boundary value problems (BVPs). Galerkin weighted residual method (GWRM) are widely used to solve BVPs. The main aim of this paper is to find the approximate solutions of fifth, seventh and ninth order nonlinear boundary value problems using GWRM. A trial function namely, Bezier Polynomials is assumed which is made to satisfy the given essential boundary conditions. Investigate the effectiveness of the current method; some numerical examples were considered. The results are depicted both graphically and numerically. The numerical solutions are in good agreement with the exact result and get a higher accuracy in the solutions. The present method is quit efficient and yields better results when compared with the existing methods. All problems are performed using the software MATLAB R2017a.