6533b85cfe1ef96bd12bd225
RESEARCH PRODUCT
Convergence in discrete Cauchy problems and applications to circle patterns
Daniel MatthesDaniel Matthessubject
Cauchy problemCauchy's convergence testConvergence (routing)MathematicsofComputing_GENERALApplied mathematicsCauchy distributionGeometry and TopologyModes of convergenceMathematicsCauchy productdescription
A lattice-discretization of analytic Cauchy problems in two dimensions is presented. It is proven that the discrete solutions converge to a smooth solution of the original problem as the mesh size ε \varepsilon tends to zero. The convergence is in C ∞ C^\infty and the approximation error for arbitrary derivatives is quadratic in ε \varepsilon . In application, C ∞ C^\infty -approximation of conformal maps by Schramm’s orthogonal circle patterns and lattices of cross-ratio minus one is shown.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-02-09 | Conformal Geometry and Dynamics of the American Mathematical Society |