Matches in SemOpenAlex for { <https://semopenalex.org/work/W1530481664> ?p ?o ?g. }
Showing items 1 to 85 of
85
with 100 items per page.
- W1530481664 abstract "For describing the probability distribution of the positions and times of particles performing anomalous motion, fractional PDEs are derived from the continuous time random walk models with waiting time distribution having divergent first order moment and/or jump length distribution which has divergent second order moment. It can be noted that the fractional PDEs are essentially dealing with the multiscale issues. Generally the regularity of the solutions for fractional PDEs is weak at the areas close to boundary and initial time. This paper focuses on developing the applications of wavelet bases to numerically solving fractional PDEs and digging out the potential benefits of wavelet methods comparing with other numerical methods, especially in the aspects of realizing preconditioning, adaptivity, and keeping the Toeplitz structure. More specifically, the contributions of this paper are as follows: 1. the techniques of efficiently generating stiffness matrix with computational cost $mathcal{O}(2^J)$ are provided for first, second, and any order bases; 2. theoretically and numerically discuss the effective preconditioner for time-independent equation and multigrid method for time-dependent equation, respectively; 3. the wavelet adaptivity is detailedly discussed and numerically applied to solving the time-dependent (independent) equations. In fact, having reliable, simple, and local regularity indicators is the striking benefit of the wavelet in adaptively solving fractional PDEs (it seems hard to give a local posteriori error estimate for the adaptive finite element method because of the global property of the operator)." @default.
- W1530481664 created "2016-06-24" @default.
- W1530481664 creator A5016786664 @default.
- W1530481664 creator A5047048001 @default.
- W1530481664 date "2015-05-05" @default.
- W1530481664 modified "2023-09-27" @default.
- W1530481664 title "Applications of Wavelet Bases to The Numerical Solutions of Fractional PDEs" @default.
- W1530481664 cites W1965197622 @default.
- W1530481664 cites W1966513244 @default.
- W1530481664 cites W1970609396 @default.
- W1530481664 cites W2002386912 @default.
- W1530481664 cites W2009063484 @default.
- W1530481664 cites W2020062189 @default.
- W1530481664 cites W2059967877 @default.
- W1530481664 cites W2064361774 @default.
- W1530481664 cites W2093739480 @default.
- W1530481664 cites W2104736025 @default.
- W1530481664 cites W2118288723 @default.
- W1530481664 cites W2401294069 @default.
- W1530481664 cites W642707038 @default.
- W1530481664 hasPublicationYear "2015" @default.
- W1530481664 type Work @default.
- W1530481664 sameAs 1530481664 @default.
- W1530481664 citedByCount "1" @default.
- W1530481664 countsByYear W15304816642015 @default.
- W1530481664 crossrefType "posted-content" @default.
- W1530481664 hasAuthorship W1530481664A5016786664 @default.
- W1530481664 hasAuthorship W1530481664A5047048001 @default.
- W1530481664 hasConcept C110121322 @default.
- W1530481664 hasConcept C121332964 @default.
- W1530481664 hasConcept C126255220 @default.
- W1530481664 hasConcept C134306372 @default.
- W1530481664 hasConcept C137119250 @default.
- W1530481664 hasConcept C154945302 @default.
- W1530481664 hasConcept C159694833 @default.
- W1530481664 hasConcept C167431342 @default.
- W1530481664 hasConcept C179254644 @default.
- W1530481664 hasConcept C28826006 @default.
- W1530481664 hasConcept C33923547 @default.
- W1530481664 hasConcept C41008148 @default.
- W1530481664 hasConcept C47432892 @default.
- W1530481664 hasConcept C74650414 @default.
- W1530481664 hasConcept C93779851 @default.
- W1530481664 hasConceptScore W1530481664C110121322 @default.
- W1530481664 hasConceptScore W1530481664C121332964 @default.
- W1530481664 hasConceptScore W1530481664C126255220 @default.
- W1530481664 hasConceptScore W1530481664C134306372 @default.
- W1530481664 hasConceptScore W1530481664C137119250 @default.
- W1530481664 hasConceptScore W1530481664C154945302 @default.
- W1530481664 hasConceptScore W1530481664C159694833 @default.
- W1530481664 hasConceptScore W1530481664C167431342 @default.
- W1530481664 hasConceptScore W1530481664C179254644 @default.
- W1530481664 hasConceptScore W1530481664C28826006 @default.
- W1530481664 hasConceptScore W1530481664C33923547 @default.
- W1530481664 hasConceptScore W1530481664C41008148 @default.
- W1530481664 hasConceptScore W1530481664C47432892 @default.
- W1530481664 hasConceptScore W1530481664C74650414 @default.
- W1530481664 hasConceptScore W1530481664C93779851 @default.
- W1530481664 hasLocation W15304816641 @default.
- W1530481664 hasOpenAccess W1530481664 @default.
- W1530481664 hasPrimaryLocation W15304816641 @default.
- W1530481664 hasRelatedWork W118802909 @default.
- W1530481664 hasRelatedWork W1715738066 @default.
- W1530481664 hasRelatedWork W1999279996 @default.
- W1530481664 hasRelatedWork W2022298739 @default.
- W1530481664 hasRelatedWork W2064785338 @default.
- W1530481664 hasRelatedWork W2155242217 @default.
- W1530481664 hasRelatedWork W2184424055 @default.
- W1530481664 hasRelatedWork W2340388657 @default.
- W1530481664 hasRelatedWork W2396013348 @default.
- W1530481664 hasRelatedWork W2564443227 @default.
- W1530481664 hasRelatedWork W2606030334 @default.
- W1530481664 hasRelatedWork W2768931472 @default.
- W1530481664 hasRelatedWork W2954403030 @default.
- W1530481664 hasRelatedWork W2969162489 @default.
- W1530481664 hasRelatedWork W3016712069 @default.
- W1530481664 hasRelatedWork W3019386315 @default.
- W1530481664 hasRelatedWork W3135522375 @default.
- W1530481664 hasRelatedWork W3135577874 @default.
- W1530481664 hasRelatedWork W3145989604 @default.
- W1530481664 hasRelatedWork W3194859423 @default.
- W1530481664 isParatext "false" @default.
- W1530481664 isRetracted "false" @default.
- W1530481664 magId "1530481664" @default.
- W1530481664 workType "article" @default.