Name
Abstract | ||
|---|---|---|
AbstractThe classical methods for solving initial-boundary-value problems for linear partial differentialequations with constant coefficients rely on separation of variables and specific integraltransforms. As such, they are limited to specific equations, with special boundary conditions. Herewe review a method introduced by Fokas, which contains the classical methods as special cases.However, this method also allows for the equally explicit solution of problems for which noclassical approach exists. In addition, it is possible to elucidate which boundary-value problemsare well posed and which are not. We provide examples of problems posed on the positive half-lineand on the finite interval. Some of these examples have solutions obtainable using classicalmethods, and others do not. For the former, it is illustrated how the classical methods may berecovered from the more general approach of Fokas. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1137/110821871 | Periodicals |
Keywords | Field | DocType |
partial differential equations,complex analysis,evolution equations | Boundary value problem,Mathematical optimization,Mathematical analysis,Constant coefficients,Numerical partial differential equations,Examples of differential equations,Integral transform,Partial differential equation,Separation of variables,Multigrid method,Mathematics | Journal |
Volume | Issue | ISSN |
56 | 1 | 0036-1445 |
Citations | PageRank | References |
2 | 0.65 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernard Deconinck | 1 | 54 | 14.39 |
| Thomas Trogdon | 2 | 6 | 3.29 |
| Vishal Vasan | 3 | 6 | 1.93 |