scholarly journals Efficient simulation of unsaturated flow using exponential time integration

2011 ◽  
Vol 217 (14) ◽  
pp. 6587-6596 ◽  
Author(s):  
E.J. Carr ◽  
T.J. Moroney ◽  
I.W. Turner
Keyword(s):  
Unsaturated Flow ◽  
Time Integration ◽  
Exponential Time ◽  
Efficient Simulation ◽  
Exponential Time Integration

scholarly journals Exponential Time Integration and Second-Order Difference Scheme for a Generalized Black-Scholes Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Zhongdi Cen ◽  
Anbo Le ◽  
Aimin Xu
Keyword(s):  
Difference Scheme ◽  
Time Integration ◽  
Second Order ◽  
Integration Scheme ◽  
Uniform Mesh ◽  
Central Difference ◽  
Exponential Time ◽  
Black Scholes ◽  
Time Integration Scheme ◽  
Exponential Time Integration

We apply an exponential time integration scheme combined with a central difference scheme on a piecewise uniform mesh with respect to the spatial variable to evaluate a generalized Black-Scholes equation. We show that the scheme is second-order convergent for both time and spatial variables. It is proved that the scheme is unconditionally stable. Numerical results support the theoretical results.

Exponential time integration using Krylov subspaces

2009 ◽  
Vol 60 (6) ◽  
pp. 591-609 ◽  
Author(s):  
J. C. Schulze ◽  
P. J. Schmid ◽  
J. L. Sesterhenn
Keyword(s):  
Time Integration ◽  
Krylov Subspaces ◽  
Exponential Time ◽  
Exponential Time Integration

Exponential Time Integration of Evolution Equations

2010 ◽  
Author(s):  
Alexander Ostermann ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Evolution Equations ◽  
Time Integration ◽  
Exponential Time ◽  
Exponential Time Integration

Fast Exponential Time Integration for Pricing Options in Stochastic Volatility Jump Diffusion Models

2014 ◽  
Vol 4 (1) ◽  
pp. 52-68 ◽  
Author(s):  
Hong-Kui Pang ◽  
Hai-Wei Sun
Keyword(s):  
Stochastic Volatility ◽  
Temporal Integration ◽  
Time Integration ◽  
Computational Cost ◽  
Jump Diffusion ◽  
Integration Scheme ◽  
Arnoldi Method ◽  
Exponential Time ◽  
Jump Diffusion Model ◽  
Exponential Time Integration

AbstractThe stochastic volatility jump diffusion model with jumps in both return and volatility leads to a two-dimensional partial integro-differential equation (PIDE). We exploit a fast exponential time integration scheme to solve this PIDE. After spatial discretization and temporal integration, the solution of the PIDE can be formulated as the action of an exponential of a block Toeplitz matrix on a vector. The shift-invert Arnoldi method is employed to approximate this product. To reduce the computational cost, matrix splitting is combined with the multigrid method to deal with the shift-invert matrix-vector product in each inner iteration. Numerical results show that our proposed scheme is more robust and efficient than the existing high accurate implicit-explicit Euler-based extrapolation scheme.

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