On the convergence of finite-difference schemes of high-order accuracy for singular problems

1994 ◽  
Vol 34 (4) ◽  
pp. 344-355 ◽  
Author(s):  
R. Čiegis
Keyword(s):  
Finite Difference ◽  
High Order ◽  
Difference Schemes ◽  
High Order Accuracy ◽  
Finite Difference Schemes ◽  
Order Accuracy ◽  
Singular Problems

scholarly journals Accurate Simulation of Contaminant Transport Using High-Order Compact Finite Difference Schemes

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Gurhan Gurarslan
Keyword(s):  
Finite Difference ◽  
Exact Solutions ◽  
Contaminant Transport ◽  
High Order ◽  
Difference Schemes ◽  
Sixth Order ◽  
High Order Accuracy ◽  
Finite Difference Schemes ◽  
Compact Finite Difference ◽  
Compact Finite Difference Schemes

Numerical simulation of advective-dispersive contaminant transport is carried out by using high-order compact finite difference schemes combined with second-order MacCormack and fourth-order Runge-Kutta schemes. Both of the two schemes have accuracy of sixth-order in space. A sixth-order MacCormack scheme is proposed for the first time within this study. For the aim of demonstrating efficiency and high-order accuracy of the current methods, some numerical experiments have been done. The schemes are implemented to solve two test problems with known exact solutions. It has been exhibited that the methods are capable of succeeding high accuracy and efficiency with minimal computational effort, by comparisons of the computed results with exact solutions.

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