In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations of the form y′′ f x, y , a x b with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids...

This study assessed the heavy metals and polycyclic aromatic hydrocarbons (PAHs) pollutant in soil around petrol filling stations automobile mechanic workshops. Samples of were acquired from depth range 0–15 cm. Toxic analyzed with atomic absorption spectrophotometry. The PAHs using phytochemical chromatographic analysis by Soxhlet extraction method. tested was weakly acidic (6.12–6.81). trend ...

The effect of conservation of integral invariants by finite-element discretization schemes of the shallow-water equations as a model for long-term integrations of atmospheric models is investigated. Two finite-element models are used. The first uses rectangular elements and conserves total energy using an intrinsic method. The second model uses triangular elements and a high-accuracy two-stage ...

Two piecewise-linearized methods for the numerical solution of nonlinear second-order differential equations which contain the first-order derivative are presented. These methods provide piecewise analytical solutions in open intervals, result in explicit finite difference equations for both the displacement and the velocity or only the displacement, at nodal points, and continuous solutions ev...

We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) n-dimensional nonhomogeneous wave equation, n? 1. Their construction is accomplished by both classical Numerov approach and alternative technique based on averaging together with further necessary improvements arising scheme 2. The applicable to other types PDEs including pa...

This study assessed the heavy metals and polycyclic aromatic hydrocarbons (PAHs) pollutant in soil around petrol filling stations automobile mechanic workshops. Samples of were acquired from depth range 0–15 cm. Toxic analyzed with atomic absorption spectrophotometry. The PAHs using phytochemical chromatographic analysis by Soxhlet extraction method. tested was weakly acidic (6.12–6.81). trend ...