scholarly journals High Order Compact Finite Difference Schemes for the Helmholtz Equation with Discontinuous Coefficients

2011 ◽  
Vol 29 (3) ◽  
pp. 324-340 ◽  
Author(s):  
Xiufang Feng
Keyword(s):  
Finite Difference ◽  
Helmholtz Equation ◽  
Discontinuous Coefficients ◽  
High Order ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Compact Finite Difference ◽  
Compact Finite Difference Schemes

scholarly journals High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation

2003 ◽  
Vol 06 (07) ◽  
pp. 767-789 ◽  
Author(s):  
Bertram Düring ◽  
Michel Fournié ◽  
Ansgar Jüngel
Keyword(s):  
Finite Difference ◽  
Transaction Costs ◽  
High Order ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Compact Schemes ◽  
Unconditionally Stable ◽  
Compact Finite Difference ◽  
Black Scholes ◽  
Compact Finite Difference Schemes

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.

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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