Recent Progress in Studies of Stability of Numerical Schemes
Applications and modeling of various phenomena in all areas of scientific research require finding numerical solutions for differential, partial differential, integral, or integro-differential equations. In addition to proving theoretical convergence and giving error estimates, stability of numerica...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/12/2692 |
| _version_ | 1797455180244975616 |
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| author | Taras I. Lakoba Sanda Micula |
| author_facet | Taras I. Lakoba Sanda Micula |
| author_sort | Taras I. Lakoba |
| collection | DOAJ |
| description | Applications and modeling of various phenomena in all areas of scientific research require finding numerical solutions for differential, partial differential, integral, or integro-differential equations. In addition to proving theoretical convergence and giving error estimates, stability of numerical methods for such operator equations is a fundamental property that it is necessary for the method to produce a valid solution. This Special Issue focuses on new theoretical and numerical studies concerning the techniques used for proving stability or instability of numerical schemes, which extend or improve known results. It also includes applications to non-linear physical, chemical, and engineering systems, arising in dynamics of waves, diffusion, or transport problems. |
| first_indexed | 2024-03-09T15:47:48Z |
| format | Article |
| id | doaj.art-89b2896c9edb464fa7c6a908287af8f5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T15:47:48Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-89b2896c9edb464fa7c6a908287af8f52023-11-24T18:21:31ZengMDPI AGSymmetry2073-89942022-12-011412269210.3390/sym14122692Recent Progress in Studies of Stability of Numerical SchemesTaras I. Lakoba0Sanda Micula1Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05405, USADepartment of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, RomaniaApplications and modeling of various phenomena in all areas of scientific research require finding numerical solutions for differential, partial differential, integral, or integro-differential equations. In addition to proving theoretical convergence and giving error estimates, stability of numerical methods for such operator equations is a fundamental property that it is necessary for the method to produce a valid solution. This Special Issue focuses on new theoretical and numerical studies concerning the techniques used for proving stability or instability of numerical schemes, which extend or improve known results. It also includes applications to non-linear physical, chemical, and engineering systems, arising in dynamics of waves, diffusion, or transport problems.https://www.mdpi.com/2073-8994/14/12/2692numerical stabilityUlam–Hyers stabilitysplit–step exponential schemenumerical schemes for stochastic differential equationsdifference schemes with interpolationKPZ equation |
| spellingShingle | Taras I. Lakoba Sanda Micula Recent Progress in Studies of Stability of Numerical Schemes Symmetry numerical stability Ulam–Hyers stability split–step exponential scheme numerical schemes for stochastic differential equations difference schemes with interpolation KPZ equation |
| title | Recent Progress in Studies of Stability of Numerical Schemes |
| title_full | Recent Progress in Studies of Stability of Numerical Schemes |
| title_fullStr | Recent Progress in Studies of Stability of Numerical Schemes |
| title_full_unstemmed | Recent Progress in Studies of Stability of Numerical Schemes |
| title_short | Recent Progress in Studies of Stability of Numerical Schemes |
| title_sort | recent progress in studies of stability of numerical schemes |
| topic | numerical stability Ulam–Hyers stability split–step exponential scheme numerical schemes for stochastic differential equations difference schemes with interpolation KPZ equation |
| url | https://www.mdpi.com/2073-8994/14/12/2692 |
| work_keys_str_mv | AT tarasilakoba recentprogressinstudiesofstabilityofnumericalschemes AT sandamicula recentprogressinstudiesofstabilityofnumericalschemes |