|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|5471513||1399037||2018||7 صفحه PDF||سفارش دهید||دانلود کنید|
We consider blow-up problems having non-monotonic singular solutions that tend to infinity at a previously unknown point. For second-, third-, and fourth-order nonlinear ordinary differential equations, the corresponding multi-parameter test problems allowing exact solutions in elementary functions are proposed for the first time. A method of non-local transformations, that allows to numerically integrate non-monotonic blow-up problems, is described. A comparison of exact and numerical solutions showed the high efficiency of this method.It is important to note that the method of non-local transformations can be useful for numerical integration of other problems with large solution gradients (for example, in problems with solutions of boundary-layer type).
Journal: Applied Mathematics Letters - Volume 76, February 2018, Pages 123-129