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Application of Projective Methods for Solving Boundary Value Problems of Differential Equations with a Small Parameter

机译:在小参数中求解微分方程边值问题的投影方法

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There are considered the alternating to perturbation technique convergence method by which the solution of operator equation (1) is same as to invert the operator L of simpler structure than L + εM and apply operator M (both processes-each) at N times. This scheme is realized for some one and two dim BVPs for DEs, for integral eq. with an irremovable singularity. For 2dim problems when mathematical models are Refined Theories in wide sense for thin-walled elastic structures in case of technical domains (rectangular, quadrant, band) there are developed special variational-projective methods by which there are solved approximately some concrete problems. Last part of this report are dedicated to the applications of Variational-Projective and Schwarz Alternative Methods for technical regions of complete geometry such as finite or unbounded crosses.
机译:考虑到交替的扰动技术会聚方法,通过该方法,操作员方程(1)的解决方案相同,以反转比L +εm更简单的结构,并在n次应用操作员M(每个过程)。对于DES的一些和两个DIM BVP来实现该方案,用于积分EQ。带有不可动摇的奇点。对于2Dim问题,当数学模型是精炼理论的薄壁弹性结构中,在技术领域(矩形,象限,频段),开发了特殊的变分项目方法,通过该方法已经解决了大约一些具体问题。本报告的最后一部分致力于改变投影和Schwarz替代方法的应用,以实现完整几何形状的技术区域,如有限或无限的十字架。

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