scholarly journals Fast and High-Order Accuracy Numerical Methods for Time-Dependent Nonlocal Problems in $${\pmb {\mathbb {R}}}^2$$

2020 ◽  
Vol 84 (1) ◽  
Author(s):  
Rongjun Cao ◽  
Minghua Chen ◽  
Michael K. Ng ◽  
Yu-Jiang Wu
Keyword(s):  
Numerical Methods ◽  
High Order ◽  
Time Dependent ◽  
High Order Accuracy ◽  
Nonlocal Problems ◽  
Order Accuracy

scholarly journals High Efficient Numerical Methods for Viscous and Nonviscous Wave Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Xiujie Lv ◽  
Jinggang Qin ◽  
Tongke Wang
Keyword(s):  
Numerical Methods ◽  
High Order ◽  
High Order Accuracy ◽  
Computational Time ◽  
Boundary Values ◽  
Order Accuracy ◽  
Efficient Simulation ◽  
High Efficient ◽  
Wave Problems ◽  
New Algorithms

This paper is concerned with accurate and efficient numerical methods for solving viscous and nonviscous wave problems. The paper first introduces a new second-order PR-ADI like scheme. For an efficient simulation, the scheme is also extended to a high-order compact PRADI like method. Both of them have the advantages of unconditional stability, less impact of the perturbing terms on the accuracy, and being convenient to compute the boundary values of the intermediates. Besides this, the compact scheme has high-order accuracy and costs less in computational time. Numerical results are presented to show the accuracy and efficiency of the new algorithms.

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