A One Step Method for the Solution of General Second Order Ordinary Differential Equations

In this paper, an implicit one step method for the numerical solution of second order initial value problems of ordinary differential equations has been developed by collocation and interpolation technique. The introduction of an o step point guaranteed the zero stability and consistency of the method. The implicit method developed was implemented as a block which gave simultaneous solutions, as well as their rst derivatives, at both o step and the step point. A comparison of our method to the predictor-corrector method after solving some sample problems reveals that our method performs better

Solving General Second Order Ordinary Differential Equations by a One-Step Hybrid Collocation Method

A one-step hybrid method is developed for the numerical approximation of second order initial value problems of ordinary differential equations by interpolation and collocation at nonstop and step points respectively. The method is zero stable and consistent with very small error term. Numerical experiment of the method on sample problem shows that the method is more efficient and accurate than the results obtained from our earlier methods

Modified Block Method for the Direct Solution of Second Order Ordinary Differential Equations

The direct solution of general second order ordinary differential equations is considered in this paper. The method is based on the collocation and interpolation of the power series approximate solution to generate a continuous linear multistep method. We modified the existing block method in order to accommodate the general nth order ordinary differential equation. The method was found to be efficient when tested on second order ordinary differential equation

Numerical Simulation of Electric Field and Charge Structure within an Isolated Thunderstorm

The study of electrical structure of thunderstorm is a deterministic factor in characterizing the behavior of lightning. It is impossible to measure the value of electric field at every point within the thunderstorm, even when the in situ measurements are made, they are done along the path of balloon-borne instruments or other methods employed in the measurement. The average data obtained from past measurements were employed in determining the electric field generated by the thunderstorm as observed along the horizontal distance using the cylindrical charge model. The data consisted of a screening charge layer firstly located “between” 1.8-2.0 km and later between 10.0-10.2 km respectively above the ground level (agl) to see the effect of positioning on the resultant computation. The lower positive charge center with radius ranging from 0.5 km to 2.0 km was placed at various heights between 2.0 and 6.0 km. This is to determine the effect of cloud base height on the resulting field profile. The main negative charge is accommodated between 4.0 and 7.5 km and the upper positive charge layer existed between 7.5- 10.0 km agl for a cloud base height of 2.0 km and 6.0- 9.5 km agl for a negative charge layer, 7.5- 11.0 km agl for upper positive charge with a cloud base of 4.0 km high. The resulting potential gradient (PG) profiles were obtained for spatial distribution with screening charge layer playing no active role in the thunderstorm electrification. The effects of wind shear due to increasing wind speed with height were also investigated to have a clear picture of the cloud charge dynamics; hence the vertical PG patterns produced by a moving thunderstorm for various cloud cell life-times were modeled. The results showed that a typical tropical thunderstorm can exhibit charge layer more than the normal tripolar structure, and the pocket of lower positive charge can be more than one or larger than the usual size. Wind shear was found to enhance lightning discharges at the surface of charge discontinuities. Keywords: Potential gradient, Wind shear, Cloud charge, Lower positive charge center, Noninductive charging.

One Step Continuous Hybrid Block Method for the Solution of y'''=f(x,y,y',y'')

In this paper, we present a block method for the direct solution of third order initial value problems of ordinary differential equations. Collocation and interpolation approach was adopted to generate a continuous linear multistep method which was then solved for the independent solution to give a continuous block method. We evaluated the result at selected grid points to give a discrete block which eventually gave simultaneous solutions at both grid and off grid points.  The one-step block method is consistent and A -stable, with good region of absolute stability. Experimental results confirmed the superiority of the new scheme over an existing method. Keywords: consistent, convergent, collocation, hybrid points, independent solution, interpolation, zero stabl

One-Step Implicit Hybrid Block Method for The Direct Solution of General Second Order Ordinary Differential Equations

A one-step implicit hybrid block solution method for initial value problems of general second order ordinary differential equations has been studied in this paper. The onestep method is augmented by the inclusion of off step points to enable the multistep procedure. This guaranteed zero stability as well as consistency of the resulting method. The convergence and weak stability properties of the new method have been established. Results from the new method compared with those obtained from existing methods show that the new method gives better accuracy

TWO STEPS BLOCK METHOD FOR THE SOLUTION OF GENERAL SECOND ORDER INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATION

In this paper, an implicit block linear multistep method for the solution of ordinary differential equation        was extended to the general form of differential equation. This method is self starting and does not        need   a   predictor   to   solve   for   the   unknown   in   the   corrector.   The   method   can   also   be   extended   to        boundary   value   problems  without   additional   cost.   The  method was   found to   be  efficient   after   being        tested with numerical problems of second order

FOUR STEPS IMPLICIT METHOD FOR THE SOLUTION OF GENERAL SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Four steps implicit scheme for the solution of second order ordinary differential equation was derived        through interpolation and collocation method. Newton polynomial approximation method was used to        generate the unknown parameters in the corrector. The method was tested with numerical examples        and it was found to be efficient in solving second order ordinary differential equations.&nbsp

Cholinesterase inhibitory activity and structure elucidation of a new phytol derivative and a new cinnamic acid ester from Pycnanthus angolensis

AbstractThe leaves of Pycnanthus angolensis (Welw.) Warb., Myristicaceae, are used as memory enhancer and anti-ageing in Nigerian ethnomedicine. This study aimed at evaluating the cholinesterase inhibitory property as well as isolates the bioactive compounds from the plant. The acetylcholinesterase and butyrylcholinesterase inhibitory potentials of extracts, fractions, and isolated compounds were evaluated by colorimetric and TLC bioautographic assay techniques. The extract inhibited both enzymes with activity increasing with purification, ethyl acetate fraction being most active fraction at 65.66±1.06% and 49.38±1.66% against acetylcholinesterase and butyrylcholinesterase, respectively while the supernatant had 77.44±1.18 inhibition against acetylcholinesterase. Two new bioactive compounds, (2E, 18E)-3,7,11,15,18-pentamethylhenicosa-2,18-dien-1-ol (named eluptol) and [12-(4-hydroxy-3-methyl-oxo-cyclopenta-1,3-dien-1yl)-11-methyl-dodecyl](E)-3-(3,4-dimethylphenyl)prop-2-enoate (named omifoate A) were isolated from the plant with IC50 of 22.26μg/ml (AChE), 34.61μg/ml (BuChE) and 6.51μg/ml (AChE), 9.07μg/ml (BuChE) respectively. The results showed that the plant has cholinesterase inhibitory activity which might be responsible for its memory enhancing action, thus justifying its inclusion in traditional memory enhancing preparation

Normal CD4, CD8 T-lymphocytes and leucocyte baseline in healthy HIV-seronegative pregnant women in Ekpoma, Edo State, Nigeria

This study was aimed at establishing the baseline values of CD4 and CD8 absolute counts among healthy pregnant women in Ekpoma, Edo State, Nigeria. Ninety (90) apparently healthy pregnant women between the age group of 18-39 years and thirty (30) non- pregnant women (control) were used as study subjects. The pregnant subjects were divided into three groups, depending on the trimester of pregnancy. CD4 and CD8 absolute counts were determined using flow cytometry. An automated blood analyzer was used to determine the leucocyte counts. The mean WBC (total) count (x103/μl) of the pregnant women was 7.71±1.76 against 4.97 ± 0.82 of the control subjects. Statistical comparison showed a statistical significance changes in the mean CD4 counts between the test and control subjects but no statistical significant difference in the total WBC and absolute CD8 counts of both groups (P>0.05). In contrast, the CD4 absolute count showed a statistical significant difference when compared with the mean values of the control subjects. In conclusion, pregnancy significantly increased the mean values of WBC count but significantly decreased CD4+ cell count when compared to nonpregnant controls while the mean CD8+ cell count did not show any difference in the subjects studied.Key words: CD4 counts, CD8 counts, Leucocytes counts, Healthy pregnant women, Ekpom