Journal of Applied & Computational Mathematics

Time series modeling and forecasting has ultimate importance in various practical domains in the world. Many significant models have been proposed to improve the accuracy of their prediction. Global warming has been a big challenge to the world in affecting the normality of the day to day economic and non-economic activities. It causes far-reaching weather changes, which are characterized by precipitation or temperature fluctuations. Rainfall prediction is one of the most important and challenging tasks in the recent today’s world. In Kenya unstable weather patterns which are associated with global warming have been experienced to a greater extent. The objective of this study was to modeled rainfall patterns in Kenya by use of Bayesian Vector Autoregressive (BVAR). To achieve this objective, the data was first statistically diagnosed using Augmented Dicker Fuller and Granger Causality test. The BVAR model was developed using multiple regression analysis in a system of equations. The model sensitivity was performed using confusion matrix and the F-test was used to compare the variances of the actual and forecasted rainfall values. After the first differencing the data was found to be stationary where Augmented Dicker Fuller (ADF) test was statistically significant with P-values <0.05. The Granger Causality test found that; temperature, atmospheric pressure, wind speed and relative humidity influenced the rainfall time series models in all the regions. The model sensitivity was performed using confusion matrix. The BVAR model developed was statistically significant (R2=0.9896). The sensitivity of the model was 82.22%, making it appropriate for forecasting. In conclusion the Bayesian Vector Autoregressive model developed is suitable and sensitive for forecasting rainfall patterns.

The study examined the influence of mobile phone on students’ interest in basic general mathematics colleges of education in Enugu state. Three research questions were posed to guide the study. The study adopted survey research design. All the NCE 1 students of government owned colleges of education in Enugu state form the population of the study. Sixty students (60) were sampled from the population using multistage sampling technique. The study sample was exposed to learning basic general mathematics (GSS 122) through mobile phone for period of three weeks. The instrument for collecting data was Basic General Mathematics Interest Questionnaire (BGMIQ) with reliability coefficient of 0.89 obtained from Cronbach alpha. Descriptive Statistic of mean and standard deviation was used to answer the research questions. It was found among others that the learning of basic general through the mobile phone develops the interest of the students in three main constructs (namely: tested, leisure and career). It was recommended among others that lecturers should be encouraged to integrate mobile phone for teaching basic general mathematics so as stimulate the interest of the students thereby improve their achievement in the course.

In this study, power series and shifted Chebyshev polynomials are used as basis function for solving first order volterra integro-differential equations using standard collocation method. An assumed approximate solution in terms of the constructed polynomial was substituted into the class of integro-differential equation considered. The resulted equation was collocated at appropriate points within the interval of consideration [0,1] to obtain a system of algebraic linear equations. Solving the system of equations, by inverse multiplication, the unknown coefficients involved in the equations are obtained. The required approximate results are obtained when the values of the constant coefficients are substituted back into the assumed approximate solution. Numerical example are presented to confirm the accuracy and efficiency of the method.

The Frobenius method, also known as the Extended Power Series method comes into play when solving second-order homogeneous linear ODEs having variable coefficients, about a singular point. The solution is expressed in terms of infinite power series. This straightforward article is merely aimed to lucidly arrive at the recurrence relation/formula by taking proper heed of summation limits and simply manipulating them, which is probably absent in almost all research articles and books. The methodology discussed is followed by a few conspicuous and relevant observations.

The episode of Coronavirus, starting in 2019 and going on through the hour of composing, has prompted reestablished interest in the numerical displaying of irresistible sickness. Late works have zeroed in on fractional differential condition (PDE) models, especially response dispersion models, ready to depict the movement of a pestilence in both reality. These examinations have shown commonly encouraging outcomes in portraying and anticipating Coronavirus movement. Be that as it may, individuals frequently travel significant distances in brief timeframes, prompting nonlocal transmission of the sickness. Such virus elements are not very much addressed by dissemination alone. Conversely, customary differential condition (Tribute) models may effortlessly represent this way of behaving by thinking about divergent locales as hubs in an organization, with the edges characterizing nonlocal transmission. In this work, we endeavor to join these demonstrating standards by means of the presentation of an organization structure inside a response dispersion PDE framework. This is accomplished through the meaning of a populace move administrator, which couples disjoint and possibly far off geographic locales, working with nonlocal populace development between them. We give scientific outcomes showing that this administrator doesn't upset the actual consistency or numerical well-posedness of the framework, and check these outcomes through mathematical tests. We then utilize this strategy to recreate the Coronavirus plague in the Brazilian district of Rio de Janeiro, exhibiting its capacity to catch significant nonlocal ways of behaving, while at the same time keeping up with the benefits of a response dissemination model for portraying neighborhood elements.