Journal of the Nigerian Mathematical Society最新文献

A new, accurate and general formula for evaluating the skin friction parameter in a Magneto-Hydrodynamics (MHD) Falkner–Skan flow over a permeable wall was obtained. The formula gives the value of the skin friction of the problem in an infinite interval $(0,\infty )$ for all various values of the parameters involved. Shooting method via Runge–Kutta method for solving two-point boundary value problem in a truncated interval $(0,L)$ is used to compare the results obtained. It was observed that the percentage difference between the two sets of results is very small.

This study was conducted to investigate the two dimensional heat transfer of a free convective MHD flow with radiation and temperature dependent heat source of a viscous incompressible fluid in a porous medium between two vertical wavy walls. The flow is assumed to consist of a mean part and a perturbed part. The perturbed quantities are expressed in terms of exponential series for short wave-length. The resultant differential equations are solved by Differential Transform Method (DTM). The numerical computations are presented graphically to show the salient features of the fluid flow and heat transfer characteristics. The skin friction and Nusselt number are also analyzed for variation of governing parameters.

The steady two-dimensional flow over a vertical stretching surface in presence of aligned magnetic field, cross-diffusion and radiation effects are considered. The governing partial differential equations are transformed to nonlinear ordinary differential equation by using similarity transformation and then solved numerically by using bvp4c with MATLAB package. The effects of various non-dimensional governing parameters on velocity, temperature, concentration profiles along friction factor, Nusselt and Sherwood numbers are discussed and presented through graphs and tables’.We observed that increase in aligned angle strengthen the magnetic field and decreases the velocity profile of the flow and enhances the heat transfer rate. Comparisons with existed results are presented.

We introduce a new class of implicit two-derivative Runge–Kutta collocation methods designed for the numerical solution of systems of equations and show how they have been implemented in an efficient parallel computing environment. We also discuss the difficulty associated with large systems and how, in this case, one must take advantage of the second derivative terms in the methods. We consider two modified versions of the methods which are suitable for solving stable systems. The first modification involves the introduction of collocation at the two end points of the integration interval in addition to the Gaussian interior collocation points and the second involves the introduction of a different class of basic second derivative methods. With these modifications, fewer function evaluations per step are achieved, resulting into methods that are cheap and easy to implement. The stability properties of these methods are investigated and numerical results are given for each of the modified version to illustrate the computational efficiency of the modified methods.

A mathematical analysis has been carried out to investigate the effects of internal heat generation/absorption, viscous and ohmic dissipations on steady two-dimensional radiative MHD boundary-layer flow of a viscous, incompressible, electrically conducting nanofluid over a vertical plate. A system of governing nonlinear PDEs is converted into a set of nonlinear ODEs by suitable similarity transformations and then solved analytically using HAM and numerically by the fourth order Runge–Kutta integration scheme with shooting method. The effects of different controlling parameters on the dimensionless velocity, temperature and nanoparticle volume fraction profiles are discussed graphically. The reduced Nusslet number and the local Sherwood number are also discussed graphically. It is found that the presence of viscous dissipation, heat generation and magnetic field accelerates the temperature and decelerates the nanosolid volume fraction profile. Furthermore, comparisons have been made with bench mark solutions for a special case and obtained a very good agreement.

Stochastic Volatility (SV) model usually assumes that the distribution of asset returns conditional on the latent volatility is normal. Previous approaches to estimation of SV model have mostly focused on Gaussian filters in practice. This paper analyzes SV model with the student-t distribution and compares the distribution with mixture-of-normal distributions of Kim and Stoffer [22]. A Sequential Monte Carlo with Expectation–Maximization (SMCEM) technique based on student-t distribution is developed to estimate the parameters for the extended volatility model. The SMC method, or particle filter based on student-t distribution, which is heavier tailed than Gaussians, provides an approximate solution to non-Gaussian estimation problem and hence more robust. Our empirical analysis indicates that extension of the SV model such as a specification of the error term with student-t distribution in the return equation dominates the normal mixture distribution. Additionally, the t-distribution based particle filter is applied to a multivariate stochastic volatility model. It is again shown that the student-t based algorithm performs quite well in explaining the joint dynamics in the volatility of a set of four exchange rates series.

A nonlinear elliptic partial differential equation (pde) is obtained as a generalization of the planar Euler equation to the surface of the sphere. A general solution of the pde is found and specific choices corresponding to Stuart vortices are shown to be determined by two parameters $\lambda$ and $N$ which characterizes the solution. For $\lambda =1$ and $N=0$ or $N=-1$, the solution is globally valid everywhere on the sphere but corresponds to stream functions that are simply constants. The solution is however non-trivial for all integral values of $N\ge 1$ and $N\le -2$. In this case, the solution is valid everywhere on the sphere except at the north and south poles where it exhibits point-vortex singularities with equal circulation. The condition for the solutions to satisfy the Gauss constraint is shown to be independent of the value of the parameter $N$. Finally, we apply the general methods of Wahlquist and Estabrook to this equation for the determination of (pseudo) potentials. A realization of this algebra would allow the determination of Bäcklund transformations to evolve more general vortex solutions than those presented in this paper.

The objective of this paper is to obtain an upper bound to the Third Hankel determinant denoted by $H_3\left(1\right)$ for certain subclass of univalent functions, using Toeplitz determinants.

This paper presents a family of Continuous Third Derivative Block Methods (CTDBM) of order $k+3$ for the solution of stiff systems of ordinary differential equations. The approach uses the collocation and interpolation technique to generate the main Continuous Third Derivative method (CTDM) which is then used to obtain the additional methods that are combined as a single block methods. Analysis of the methods show that the method is L-stable up to order eight. Numerical examples are given to illustrate the accuracy and efficiency of the proposed method.

Minimum Message Length MML87 is an information theoretical criterion for model selection and point estimation. In principle, it is a method of inductive inference, and is used in a wide range of approximations and algorithm to determine the ideal model for any given data. In this study, MML87 model selection criterion was investigated and compared with other notably model selection criteria such as Akaike information criterion (AIC), Bayesian information criterion (BIC), Corrected Akaike information criterion (AICc), and Hannan–Quinn (HQ), using Bootstrap Simulation Technique to simulate autoregressive model of order $P$. We specified three different counts systems as under inferred, correctly inferred and over inferred. Based on the candidate model explored with autoregressive model and the aggregate true model explored, with the estimated parameters. MML87 performed better than all other model selection criteria through the negative log likelihood function and the mean square prediction error estimated. It is more efficient and correctly inferred.