scholarly journals Error Estimates of Energy Stable Numerical Schemes for Allen–Cahn Equations with Nonlocal Constraints

2018 ◽  
Vol 79 (1) ◽  
pp. 593-623 ◽  
Author(s):  
Shouwen Sun ◽  
Xiaobo Jing ◽  
Qi Wang
Keyword(s):  
Error Estimates ◽  
Numerical Schemes ◽  
Energy Stable ◽  
Nonlocal Constraints

Energy Stable Numerical Schemes for Ternary Cahn-Hilliard System

2020 ◽  
Vol 84 (2) ◽  
Author(s):  
Wenbin Chen ◽  
Cheng Wang ◽  
Shufen Wang ◽  
Xiaoming Wang ◽  
Steven M. Wise
Keyword(s):  
Numerical Schemes ◽  
Energy Stable

A Numerical Method and its Error Estimates for the Decoupled Forward-Backward Stochastic Differential Equations

2014 ◽  
Vol 15 (3) ◽  
pp. 618-646 ◽  
Author(s):  
Weidong Zhao ◽  
Wei Zhang ◽  
Lili Ju
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Error Estimates ◽  
Backward Stochastic Differential Equations ◽  
Second Order ◽  
Numerical Schemes ◽  
Reference Equations ◽  
Taylor Scheme ◽  
Theoretical Results

AbstractIn this paper, a new numerical method for solving the decoupled forward-backward stochastic differential equations (FBSDEs) is proposed based on some specially derived reference equations. We rigorously analyze errors of the proposed method under general situations. Then we present error estimates for each of the specific cases when some classical numerical schemes for solving the forward SDE are taken in the method; in particular, we prove that the proposed method is second-order accurate if used together with the order-2.0 weak Taylor scheme for the SDE. Some examples are also given to numerically demonstrate the accuracy of the proposed method and verify the theoretical results.

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