Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problem

Sansevieriatrifasciata was studied as a potential biosorbent for chromium, copper and nickel removal in batch process from electroplating and tannery effluents. Different parameters influencing the biosorption process such as pH, contact time, and amount of biosorbent were optimized while using the 80 mm sized particles of the biosorbent. As high as 91.3 % Ni and 92.7 % Cu were removed at pH of 6 and 4.5 respectively, while optimum Cr removal of 91.34 % from electroplating and 94.6 % from tannery effluents was found at pH 6.0 and 4.0 respectively. Pseudo second order model was found to best fit the kinetic data for all the metals as evidenced by their greater R2 values. FTIR characterization of biosorbent revealed the presence of carboxyl a

Scheduling Timetables for courses in the big departments in the universities is a very hard problem and is often be solved by many previous works although results are partially optimal. This work implements the principle of an evolutionary algorithm by using genetic theories to solve the timetabling problem to get a random and full optimal timetable with the ability to generate a multi-solution timetable for each stage in the collage. The major idea is to generate course timetables automatically while discovering the area of constraints to get an optimal and flexible schedule with no redundancy through the change of a viable course timetable. The main contribution in this work is indicated by increasing the flexibility of generating opti

This paper presents new modification of HPM to solve system of 3 rd order PDEs with initial condition, for finding suitable accurate solutions in a wider domain.

This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.