کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
472389 | 698711 | 2008 | 21 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Accurate and approximate analytic solutions of singularly perturbed differential equations with two-dimensional boundary layers Accurate and approximate analytic solutions of singularly perturbed differential equations with two-dimensional boundary layers](/preview/png/472389.png)
In this paper we construct three new test problems, called Models A, B and C, whose solutions have two-dimensional boundary layers. Approximate analytic solutions are found for these problems, which converge rapidly as the number of terms in their expansion increases. The approximations are valid for ϵ=10−8ϵ=10−8 in practical computations. Surprisingly, the algorithm for Model A can be carried out even for ϵ→∞ϵ→∞. Model C has a simple exact solution. These three new accurate and approximate analytic solutions with two-dimensional boundary layers may be more useful for testing numerical methods than those in [Z.C. Li, H.Y. Hu, C.H. Hsu, S. Wang, Particular solutions of singularly perturbed partial differential equations with constant coefficients in rectangular domains, I. Convergence analysis, J. Comput. Appl. Math. 166 (2004) 181–208] in the sense that the series solutions from the former converge much faster than those of the latter when ϵϵ is small.
Journal: Computers & Mathematics with Applications - Volume 55, Issue 11, June 2008, Pages 2602–2622