scholarly journals A high order time discretization of the solution of the non-linear filtering problem

2019 ◽  
Vol 8 (4) ◽  
pp. 693-760 ◽  
Author(s):  
Dan Crisan ◽  
Salvador Ortiz-Latorre
Keyword(s):  
Time Discretization ◽  
High Order ◽  
Linear Filtering ◽  
Non Linear ◽  
High Order Time ◽  
Filtering Problem

scholarly journals Multilevel particle filters for the non-linear filtering problem in continuous time

2020 ◽  
Vol 30 (5) ◽  
pp. 1381-1402
Author(s):  
Ajay Jasra ◽  
Fangyuan Yu ◽  
Jeremy Heng
Keyword(s):  
Continuous Time ◽  
Particle Filters ◽  
Linear Filtering ◽  
Non Linear ◽  
Filtering Problem

Experimental validation of high-order time integration for non-linear heat transfer problems

2011 ◽  
Vol 48 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Karsten J. Quint ◽  
Stefan Hartmann ◽  
Steffen Rothe ◽  
Nicolas Saba ◽  
Kurt Steinhoff
Keyword(s):  
Heat Transfer ◽  
Experimental Validation ◽  
Time Integration ◽  
High Order ◽  
Linear Heat ◽  
Non Linear ◽  
High Order Time ◽  
Transfer Problems

Two high-order time discretization schemes for subdiffusion problems with nonsmooth data

2020 ◽  
Vol 23 (5) ◽  
pp. 1349-1380
Author(s):  
Yanyong Wang ◽  
Yubin Yan ◽  
Yan Yang
Keyword(s):  
Time Discretization ◽  
Fixed Time ◽  
High Order ◽  
Transform Method ◽  
Order Of Accuracy ◽  
Nonsmooth Data ◽  
High Order Schemes ◽  
Discretization Schemes ◽  
High Order Time ◽  
Convergence Orders

Abstract Two new high-order time discretization schemes for solving subdiffusion problems with nonsmooth data are developed based on the corrections of the existing time discretization schemes in literature. Without the corrections, the schemes have only a first order of accuracy for both smooth and nonsmooth data. After correcting some starting steps and some weights of the schemes, the optimal convergence orders O(k 3–α ) and O(k 4–α ) with 0 < α < 1 can be restored for any fixed time t for both smooth and nonsmooth data, respectively. The error estimates for these two new high-order schemes are proved by using Laplace transform method for both homogeneous and inhomogeneous problem. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

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