Applied Numerical Mathematics 61 (February 2011)

IFC_[first_author]_2011_Applied-Numerical-Mathematics......Page 1
Introduction......Page 2
Implicit Runge-Kutta methods and Stein matrix equations......Page 3
The block Arnoldi algorithm......Page 5
The block Arnoldi algorithm for Stein equations......Page 6
Example 1: The nonlinear multi-mode problem......Page 8
Example 2......Page 9
Example 3: Heat equation......Page 10
Conclusion......Page 11
References......Page 12
Introduction......Page 13
Deterministic economical Runge-Kutta scheme......Page 14
Stochastic Runge-Kutta schemes......Page 15
Economical stochastic Runge-Kutta methods......Page 16
Stability regions......Page 18
Numerical results......Page 20
References......Page 22
Introduction......Page 23
The MLS approximation scheme......Page 24
Finite difference approximations......Page 25
Local weak formulation and numerical implementation......Page 26
Algorithm A......Page 27
Algorithm B......Page 28
Numerical experiments......Page 29
Conclusions......Page 31
References......Page 32
Introduction......Page 34
Continuous problem of the parabolic equation......Page 35
A posteriori error estimates of the state equation......Page 39
A posteriori error estimate of co-state equation......Page 41
Convection diffusion problem......Page 44
Hyperbolic problem......Page 48
References......Page 53
Introduction......Page 54
A fully semi-discrete Galerkin approximation......Page 56
The stability analysis......Page 58
A supraconvergent estimate......Page 61
Numerical results......Page 65
Conclusions......Page 66
References......Page 67
Introduction......Page 69
Motivation......Page 71
An improved Goldstein's type method for co-coercive VVIs with known co-coercive modulus......Page 73
A self-adaptive Goldstein's type method for VVIs with unknown co-coercive modulus......Page 75
Numerical experiments......Page 78
References......Page 80
Introduction......Page 82
Convergence of WR method......Page 83
Superlinear convergence of WR method......Page 86
Numerical experiments......Page 89
References......Page 92
Introduction......Page 94
Optimal execution......Page 95
Problem formulation: details......Page 96
Objective function: efficient frontier......Page 97
Determination of optimal control......Page 98
Similarity reduction......Page 99
Determination of the optimal control......Page 100
Discretization: an informal approach......Page 101
Discrete similarity reduction......Page 103
Optimal liquidation example: short trading horizon......Page 104
Optimal strategy: uniqueness......Page 105
Discrete trade rates......Page 107
Liquidation example: long trading horizon......Page 108
Conclusion......Page 109
Some preliminary results......Page 110
Consistency......Page 111
Monotonicity......Page 115
Convergence of the expected value......Page 116
References......Page 117
Introduction......Page 119
Euler scheme......Page 120
Numerical results......Page 121
Numerical results......Page 125
Regularization technique......Page 129
Euler and CN schemes......Page 130
Numerical results......Page 131
Discussion and conclusion......Page 135
Definition of the filters used......Page 136
References......Page 137