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

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

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

ANTI-INFLAMMATORY EFFECT OF ZINGIBER OFFICINALE ON SPRAGUE DAWLEY RATS

ABSTRACTObjective: To investigate the anti-inflammatory effect of aqueous extract of Zingiber officinale on carrageenan-induced inflammation on SpragueDawley (SD) rats.Methods: SD rats were divided into six of five groups and allowed to acclimatize for 1 week. Inflammation was induced on the animal by injecting theright hand paw with carrageenan (0.1 ml of 1%). Group 1 was given normal saline and served as a control. Group 2 was fed with food and water andserved as the carrageenan control. Group 3 was given 200 mg/kg aqueous extract of ginger, Group 4 with 400 mg/kg aqueous extract of ginger, andGroup 5 with 150 mg/kg diclofenac sodium (reference drug for inflammation).Results: The paw edema in carrageenan-induced SD rats was considerably reduced by treating with 400 mg/kg aqueous ginger extracts whencompared to the untreated SD rats (p<0.001).Conclusion: This study indicates that aqueous extract of Z. officinale possesses anti-inflammatory properties.Keywords: Anti-inflammatory, Sprague Dawley rats, Zingiber officinale, Carrageenan, Edem