Quartic Non-Polynomial Spline for Solving the Third-Order Dispersive Partial Differential Equation

In the present paper, we introduce a non-polynomial quadratic spline method for solving third-order boundary value problems. Third-order singularly perturbed boundary value problems occur frequently in many areas of applied sciences such as solid mechanics, quantum mechanics, chemical reactor theory, Newtonian fluid mechanics, optimal control, convection-diffusion processes, hydrodynamics, aerodynamics, etc. These problems have various important applications in fluid dynamics. The procedure involves a reduction of a third-order partial differential equation to a first-order ordinary differential equation. Truncation errors are given. The unconditional stability of the method is analysed by the Von-Neumann stability analysis. The developed method is tested with an illustrated example, and the results are compared with other methods from the literature, which shows the applicability and feasibility of the presented method. Furthermore, a graphical comparison between analytical and approximate solutions is also shown for the illustrated example.

高师地理专业教育实习模式研究

教育实习是突出师范特色的一个重要实践环节 ,对于培养合格师资具有重要意义 .以现代教育、教学理论为指导 ,结合目前高师院校的院系调整和课程配置改革 ,借鉴以往的教育实习实践 ,认为采取多样化的实习方式 ,有利于提高实习质量和实习的实效性 ,并对高师地理专业的部分委托实习、分散回乡实习。