Name
Title | ||
|---|---|---|
Accurate and approximate analytic solutions of singularly perturbed differential equations with two-dimensional boundary layers |
Abstract | ||
|---|---|---|
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 @e=10^-^8 in practical computations. Surprisingly, the algorithm for Model A can be carried out even for @e-~. 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 @e is small. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.camwa.2007.10.027 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
differential equation,boundary layer,convergence rates,singularly perturbed equation,former converge,model c,new test problem,s. wang,model a,approximate analytic solutions,approximate analytic solution,two-dimensional boundary layer,computational models,constant coefficient,j. comput,convergence analysis,partial differential equation,computer model,numerical method,analytic solution,exact solution,convergence rate | Convergence (routing),Exact solutions in general relativity,Differential equation,Order of accuracy,Mathematical optimization,Mathematical analysis,Constant coefficients,Numerical analysis,Partial differential equation,Mathematics,Method of matched asymptotic expansions | Journal |
Volume | Issue | ISSN |
55 | 11 | Computers and Mathematics with Applications |
Citations | PageRank | References |
3 | 0.45 | 1 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zi-Cai Li | 1 | 125 | 18.79 |
| Heng-Shuing Tsai | 2 | 3 | 0.45 |
| Song Wang | 3 | 71 | 6.80 |
| John J. H. Miller | 4 | 4 | 0.80 |