Phase-Fitted and Amplification-Fitted Higher Order Two-Derivative Runge-Kutta Method for the Numerical Solution of Orbital and Related Periodical IVPs

A phase-fitted and amplification-fitted two-derivative Runge-Kutta (PFAFTDRK) method of high algebraic order for the numerical solution of first-order Initial Value Problems (IVPs) which possesses oscillatory solutions is derived. We present a sixth-order four-stage two-derivative Runge-Kutta (TDRK) method designed using the phase-fitted and amplification-fitted property. The stability of the new method is analyzed. The numerical experiments are carried out to show the efficiency of the derived methods in comparison with other existing Runge-Kutta (RK) methods

Stress intensity factor for multiple inclined or curved cracks problem in circular positions in plane elasticity

The problems of multiple inclined or curved cracks in circular positions is treated by using the hypersingular integral equation method. The cracks center are placed at the edge of a virtual circle with radius R. The first crack is fixed on the x-axis while the second crack is located on the boundary of a circle with the varying angle, θ. A system of hypersingular integral equations is formulated and solved numerically for the stress intensity factor (SIF). Numerical examples demonstrate the effect of interaction between two cracks in circular positions are given. It is found that, the severity at the second crack tips are significant when the ratio length of the second to the first crack is small and it is placed at a small angle of θ

Numerical computation of third order delay differential equations by using direct multistep method

This paper introduces a direct multistep method to solve third order delay differential equations (DDEs) based on the boundary conditions given. The multistep method is presented in direct integration approach to reduce the total function calls involved and the method is derived implicitly so that the accuracy is attained. The method is also in block for every iteration to reduce total steps taken. The DDEs involve the endpoints of boundary conditions, hence, the shooting technique is to choose for the best value of additional initial value. The constant and pantograph delay types are the DDEs problems considered in this study. Lagrange interpolation is used to interpolate the delay involved in pantograph problems. The observation of the multistep method in terms of order, consistency, and convergence is also presented in this paper. The numerical results obtained are compared with the previous multistep method to verify the capability of the proposed method to solve third order DDEs directly

Boole's strategy in multistep block method for Volterra integro-differential equation

This article presents a numerical approach for solving the second kind of Volterra integro- differential equation (VIDE). The multistep block-Boole's rule method will estimate the solutions for the linear and nonlinear problems of VIDE. The method computes two solutions for VIDE along the interval. The proposed method is developed by derivation of the Lagrange interpolating polynomial. The convergence and stability analysis of the derived method are discussed. From the perspective of total function calls and time-saving, the computation results explained that the derived method performs better than other existing methods

Developing a Local Neurofuzzy Model for Short-Term Wind Power Forecasting

Large scale integration of wind generation capacity into power systems introduces operational challenges due to wind power uncertainty and variability. Therefore, accurate wind power forecast is important for reliable and economic operation of the power systems. Complexities and nonlinearities exhibited by wind power time series necessitate use of elaborative and sophisticated approaches for wind power forecasting. In this paper, a local neurofuzzy (LNF) approach, trained by the polynomial model tree (POLYMOT) learning algorithm, is proposed for short-term wind power forecasting. The LNF approach is constructed based on the contribution of local polynomial models which can efficiently model wind power generation. Data from Sotavento wind farm in Spain was used to validate the proposed LNF approach. Comparison between performance of the proposed approach and several recently published approaches illustrates capability of the LNF model for accurate wind power forecasting

Interaction Between Two Inclined Cracks In Bonded Dissimilar Materials

The interaction between two inclined cracks subjected to remote tension lying in the upper half of bonded dissimilar materials is considered. The hypersingular integral equation for the problem is formulated using the complex variable function method with the crack opening displacement function as the unknown and the tractions along the crack as the right-hand term. The appropriate quadrature formulas are applied in solving the hypersingular integral equation for the unknown function. Numerical results showed that the nondimensional stress intensity factor depends on the position of the cracks and the elastic constants rati

Stress intensity factor for multiple inclined or curved cracks problem in circular positions in plane elasticity

The problems of multiple inclined or curved cracks in circular positions is treated by using the hypersingular integral equation method. The cracks center are placed at the edge of a virtual circle with radius R. The first crack is fixed on the x‐axis while the second crack is located on the boundary of a circle with the varying angle, θ. A system of hypersingular integral equations is formulated and solved numerically for the stress intensity factor (SIF). Numerical examples demonstrate the effect of interaction between two cracks in circular positions are given. It is found that, the severity at the second crack tips are significant when the ratio length of the second to the first crack is small and it is placed at a small angle of θ

Health Risk Assessment of Organochlorine Pesticides Contaminations in Dairy Products from Selected Farms in Greater Accra Region-Ghana

The study was geared towards ascertaining the levels of synthetic pyrethroids and organochlorine pesticides residues in dairy products(milk, cheese and yoghurt) from selected farms in Greater Accra Region of Ghana. In all fifty (50) samples of dairy products (25 fresh cow milk, 9 cheese and 16 yoghurt) were analyzed. Detectable levels of organochlorine pesticides,OCPs(β-HCH, endrin, endosulfan, p’p’-DDT, heptachlor and methoxychlor) and Synthetic pyrethroids(permethrin, allethrin, cypermethrin, deltamethrin and cyfluthrin). Ultrasonic extraction was employed and extract clean-up was done using silica gel and analyzed using a gas chromatograph (Agilent Model 6890 Gas Chromatograph) equipped with Ni-63 electron capture detector (ECD). . Milk samples were found to be the most contaminated with respect to the OCPs and the levels ranged between 0.0001μg/ml and 0.0407μg/ml. β-HCH was the highest OCP with concentration of 0.0407μg/ml while Cyfluthrin was the highest synthetic pyrethroids recorded in yoghurt sample (0.0318μg/ml).The levels of organochlorine pesticide residues detected in all the tissues were below the accepted Maximum Residue Limits (MRL), as adopted by the WHO/FAO Codex Alimentarius Commission (2005). Keywords: dairy products, organochlorine pesticides, synthetic pyrethroid, health risk, Ghana, gas chromatograph

Stress intensity factors for a crack in bonded dissimilar materials subjected to various stresses

The modified complex variable function method with the continuity conditions of the resultant force and displacement function are used to formulate the hypersingular integral equations (HSIE) for an inclined crack and a circular arc crack lies in the upper part of bonded dissimilar materials subjected to various remote stresses. The curve length coordinate method and appropriate quadrature formulas are used to solve numerically the unknown crack opening displacement (COD) function and the traction along the crack as the right hand term of HSIE. The obtained COD is then used to compute the stress intensity factors (SIF), which control the stability behavior of bodies or materials containing cracks or flaws. Numerical results showed the behavior of the nondimensional SIF at the crack tips. It is observed that the nondimensional SIF at the crack tips depend on the various remote stresses, the elastic constants ratio, the crack geometries and the distance between the crack and the boundary

Hybrid methods for solving special fourth order ordinary differential equations

In recent time, Runge-Kutta methods that integrate special fourth or- der ordinary differential equations (ODEs) directly are proposed to ad- dress efficiency issues associated with classical Runge-Kutta methods. Although, the methods require approximation of y′, y′′ and y′′′ of the solution at every step. In this paper, a hybrid type method is proposed, which can directly integrate special fourth order ODEs. The method does not require the approximation of any derivatives of the solution. Algebraic order conditions of the methods are derived via Taylor series technique. Using the order conditions, eight algebraic order method is presented. Absolute stability of the method is analyzed and the stabil- ity region presented. Numerical experiment is conducted on some test problems. Results from the experiment show that the new method is more efficient and accurate than the existing Runge-Kutta and hybrid methods with similar number of function evaluation