An efficient approach for the numerical solution of the Monge–Ampère equation
| Autor: | Robert D. Russell, Mohamed H. M. Sulman, J. F. Williams |
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| Rok vydání: | 2011 |
| Předmět: |
Numerical Analysis
Mathematics::Complex Variables Applied Mathematics Mathematical analysis Mathematics::Analysis of PDEs Order of accuracy Monge–Ampère equation Parabolic partial differential equation Stiff equation Computational Mathematics Nonlinear system Elliptic partial differential equation Uniqueness Mathematics Numerical stability |
| Zdroj: | Applied Numerical Mathematics. 61:298-307 |
| ISSN: | 0168-9274 |
| Popis: | In this paper, we present a new method to compute the numerical solution of the elliptic Monge-Ampere equation. This method is based on solving a parabolic Monge-Ampere equation for the steady state solution. We study the problem of global existence, uniqueness, and convergence of the solution of the fully nonlinear parabolic PDE to the unique solution of the elliptic Monge-Ampere equation. Some numerical experiments are presented to show the convergence and the regularity of the numerical solution. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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