Numerov solution of linear second order ordinary differential equations containing first order derivative term

A central activity in the numerical solution of differential equations is that of finding effective numerical methods to solve particular types of problems. One of such problems is the second order ordinary differential equations of the form ′′=(,). A very important algorithm towards the solution of this equation is the Numerov method. In this present work, the Numerov method is employed to solve linear second order ordinary differential equations involving a first derivative term. By a transformation of the equation, the first derivative term is eliminated by representing it with finite difference quotient at the grid points, resulting in an equation that makes it suitable for solution. Once this equation is solved, the approximate solution of the desired function () can be obtained at the grid points. Extensive numerical tests to illustrate the effectiveness and reliability of the method are presented. The numerical experiments were conducted using Maple 2019.0 software package

Modified successive overrelaxation (SOR) type methods for M-matrices

The SOR is a basic iterative method for solution of the linear system =. Such systems can easily be solved using direct methods such as Gaussian elimination. However, when the coefficient matrix is large and sparse, iterative methods such as the SOR become indispensable. A new preconditioner for speeding up the convergence of the SOR iterative method for solving the linear system = is proposed. Arising from the preconditioner, two new preconditioned iterative techniques of the SOR method are developed. The preconditioned iterations are applied to the linear system whose coefficient matrix is an −matrix. Convergence of the preconditioned iterations is established through standard procedures. Numerical examples and results comparison are in conformity with the analytic results. More so, it is established that the spectral radii of the proposed preconditioned SOR 1 and 2 are less than that of the classical SOR, which implies faster convergence

A new modified preconditioned accelerated overrelaxation (AOR) iterative method for L-Matrix linear algebraic systems

A new preconditioner of the type =+̅+′ which generalizes the preconditioners of Evans et al. (2001) and Ndanusa and Adeboye (2012) is proposed. Theoretical investigation of the new preconditioned AOR method is undertaken by advancement of some convergence theorems with well-known procedures. In order to validate the results of theoretical convergence analysis, numerical investigation with sample problems is done. Numerical results of comparison of the proposed preconditioner with some available preconditioners in literature are presented. The results show that convergence of the proposed preconditioned AOR method is faster than that of the unpreconditioned AOR as well as the preconditioned methods in current use

A REVIEW ON THE PHARMACOLOGICAL AND TRADITIONAL PROPERTIES OF MIMOSA PUDICA

Consumption of fruits and vegetables fight against oxidative damage by inhibiting or reducing free radicals and reactive oxygen species. Mimosa pudica is a perennial herb and belongs to the family Fabaceae. Epidemiological studies have shown that M. pudica contains metabolites such as phenols and flavonoid compounds which possess pharmacological properties such as antidiabetic, antimicrobial, antiulcer, antidepressants and anti-inflammatory. Ecological studies have shown that M. pudica grows in all types of soil which can survive in soil with low nutrient concentration. It usually requires disturbed soil to establish itself. It is commonly seen in the wastelands and along roadsides, which is an ethnomedical plant that may be used in managing various types of disease. Valuable information and literature on M. pudica are analysed and consulted using a different database such as Google Scholar, Google, Science Direct, Web of Science, Academic Journals and Pubmed. This review article summarises the pharmacological properties of M. pudica

Hybrid approach on multi- spatiotemporal data framework towards analysis of long-lead upstream flood: a case of Niger State, Nigeria

Floods have become a global concern because of the vast economic and ecological havoc that ensue. Thus, a flood risk mitigation strategy is used to reduce flood-related consequences by a long-lead identification of its occurrence. A wide range of causative factors, including the adoption of hybrid multi-spatiotemporal data framework is considered in implementing the strategy. Besides the structural or homogenous non-structural factors, the adoption of various Information Systems-based tools are also required to accurately analyse the multiple natural causative factors. Essentially, this was needed to address the inaccurate flood vulnerability classifications and short time of flood prediction. Thus, this study proposes a framework named: Hybrid Multi-spatiotemporal data Framework for Long-lead Upstream Flood Analysis (HyM-SLUFA) to provide a new dimension on flood vulnerability studies by uncovering the influence of multiple factors derived from topography, hydrology, vegetal and precipitation features towards regional flood vulnerability classification and long-lead analysis. In developing the proposed framework, the spatial images were geometrically and radiometrically corrected with the aid of Quantum Geographic Information System (QGIS). The temporal data were cleaned by means of winsorization methods using STATA statistical tool. The hybrid segment of the framework classifies flood vulnerability and performs long-lead analysis. The classification and analysis were conducted using the corrected spatial images to acquire better understanding on the interaction between the extracted features and rainfall in inducing flood as well as producing various regional flood vulnerabilities within the study area. Additionally, with the aid of regression technique, precipitation and water level data were used to perform long-lead flood analysis to provide a foresight of any potential flooding event in order to take proactive measures. As to confirm the reliability and validity of the proposed framework, an accuracy assessment was conducted on the outputs of the data. This study found the influence of various Flood Causative Factors (FCFs) used in the developed HyM-SLUFA framework, by revealing the spatial disparity indicating that the slope of a region shows a more accurate level of flood vulnerability compared to other FCFs, which generally causes severe upstream floods when there is low volume of precipitation within regions of low slope degree. Theoretically, the HyM-SLUFA will serve as a guide that can be adopted or adapted for similar studies. Especially, by considering the trend of precipitation and the pattern of flood vulnerability classifications depicted by various FCFs. These classifications will determine the kind(s) of policies that will be implemented in town planning, and the Flood Inducible Precipitation Volumes can provide a foresight of any potential flooding event in order to take practical proactive measures by the local authority

Fabrication and Characterization of Locally Woven Polyester Fibre Reinforced Polyester Composites

Properties of composite moulded using locally woven polyester fibre werestudied. The results showed that though properties of polyester resin were improved upon, but were far lower than composites obtained using fibre such as glass. The density of the composite was low compared to glass fibre reinforced composite. The composite moulded at pressure of 388.132kN/m2has the best properties; tensile strength 85MN/m2, modulus of elasticity 1.846GN/m2, impact strength 227.5kJ/m2 and modulus of rupture 9.910GN/m2

Numerical solution of third order three-point boundary value problems of ordinary differential equations with variable coefficients using variational-composite hybrid fixed point iterative method

This paper explores variational–composite hybrid fixed point iterative scheme for the solution of third order three-point boundary value problems. The method shows a strong convergence which makes it an efficient and reliable technique for finding approximate analytical solutions for third order three-point boundary value problems of ordinary differential equations with variable coefficients. From the numerical experiments carried out, the accuracy of the method was confirmed through the order of convergence obtained

MULTI-DIMENSIONAL MODEL FOR FLOOD VULNERABILITY ASSESSMENT IN MOKWA: A CASE OF DOWNSTREAM COMMUNITIES OF KAINJI DAM, NIGER STATE, NIGERIA

One of the most devastating and expensive natural hazards in the world today is flooding. Hence, several attempts have been made by different scholars and researchers across the globe and in Nigeria to study flood vulnerability. These studies focused on assessing either the physical or social components of vulnerability without a holistic assessment of all vulnerability components. A multi-dimensional approach to flood risk assessment is required to provide a holistic view of residents’ degree of vulnerability to flooding. However, where the multidimensional approach was adopted the result were aggregated and not localized to specific areas. Therefore, this study attempts to quantify the vulnerability indicators using the participatory approach and develop a multi-dimensionalapproach for flood vulnerability assessment in Mokwa, Nigeria. Vulnerability was explored through the lens of four dimensions (economic, environmental, physical, and social) and eighteen indicators. The indicators were scrutinized and standardized for easy aggregation and comparability. The indicators were weighted unequally using Analytical Hierarchical Process (AHP). Nine communities and 382 households were selected purposively from the downstreamarea of the Kainji dam for sampling. The data collected were subjected to descriptive and inferential statistics using XLSTAT (2014) and spatial analysis in ARCGIS 10.7 environment. The flood vulnerability index revealed that the communities experienced high flood vulnerability from all dimensions; economic (0.71), physical (0.66), social (0.62), and environmental (0.57). The study reported a multi-dimensional flood vulnerability index of 0.65, which implies a high level of vulnerability to flooding. This study has found significant variations in all dimensions of vulnerability among the communities. The study concludes that the multi-dimensional approach to flood vulnerability provides information on the vulnerable population as well as the factors driving vulnerability in the area. The study recommends the use of a multi-dimensional approach, sophisticated models, site-specific indicators, and fine-resolution satellite data for future vulnerability assessment