We apply nonlocal symmetry-like operators to systems of two first and two second-order ordinary differential equations to seek reduction to quadratures. The reduction of order of such systems is carried out with the help of analytic continuation of scalar equations in the complex plane. Examples are taken from the literature. Precisely it is shown how the reduction to quadratures of a system of...

The present study was conducted to further improve the practice of written corrective feedback by integrating the two known feedback types (i.e. direct corrective feedback and metalinguistic explanation). With this aim, a sample of sixty-nine high-intermediate Iranian EFL learners was assigned into different feedback groups. While the first and second groups received direct and metalinguistic e...

this article proposes a direct method for solving three types of integral equations with time delay. by using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. numerical examples shows that the proposed scheme have a suitable degree of accuracy.

Sharp wave treatment for 1-D gas dynamic problem is still a chellenge modern numerical methods. They often require too many space and time steps, produce spurious oscillation of solution, exhibit strong dissipation or divergence results. This paper further extension authors’ idea employment the analytical solution coordinate, where step parameter which used in solution. Its peculiarity consists...

Foreign Direct Investment (FDI) is frequently regarded as a key driver of global economic integration because it brings job opportunities, capital investment, and business experience. The current study examines the impact of foreign direct investment on Afghanistan's economic growth using time-series data from 2007 to 2019, which are collected from the World Bank and the International Monetary ...

The direct implicit method with a second-order implicit integration scheme is formulated for and applied to the electron parallel nonlinearity in global electrostatic gyrokinetic particle-in-cell simulations of toroidal fusion plasmas. The method shows improved numerical accuracy and stability properties compared to the direct implicit method with a first-order integration scheme. The conservat...

in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...