Kimura, M. Accurate numerical scheme for the flow by curvature. (English) Zbl 0792.65100 Appl. Math. Lett. 7, No. 1, 69-73 (1994). Summary: An accurate finite difference scheme for the flow by curvature in \(\mathbb{R}^ 2\) is presented, and its convergence theorem is stated. The numerical scheme has a correction term which is effective in locating points uniformly and the effect prevents the computation from breaking down. Cited in 8 Documents MSC: 65Z05 Applications to the sciences 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35K05 Heat equation 35R35 Free boundary problems for PDEs Keywords:numerical example; moving boundary problems; finite difference scheme; flow by curvature; convergence PDF BibTeX XML Cite \textit{M. Kimura}, Appl. Math. Lett. 7, No. 1, 69--73 (1994; Zbl 0792.65100) Full Text: DOI References: [1] Gage, M.; Hamilton, R.S., The heat equation shrinking convex plane curves, J. diff. geom., 23, 69-96, (1986) · Zbl 0621.53001 [2] Grayson, M.A., The heat equation shrinks embedded plane curves to round points, J. diff. geom., 26, 285-314, (1987) · Zbl 0667.53001 [3] Ikeda, T.; Kobayashi, R., Numerical approach to interfacial dynamics, Proceedings of workshop on nonlinear PDEs and applications, (1989), (to appear) [4] Dziuk, G., An algorithm for evolutionary surfaces, Numer. math., 58, 603-611, (1991) · Zbl 0714.65092 [5] Osher, S.; Sethian, J.A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. comput. phys., 79, 12-49, (1988) · Zbl 0659.65132 [6] Sethian, J.A., Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws, J. diff. geom., 31, 131-161, (1990) · Zbl 0691.65082 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.