Preface
Prologue
Brownian Motion and Stochastic Calculus
Numerical Methods for Stochastic Differential Equations
Part I Stochastic Ordinary Differential Equations
Numerical Schemes for SDEs with Time Delay Using the Wong-Zakai Approximation
Balanced Numerical Schemes for SDEs with non-Lipschitz Coefficients
Part II Temporal White Noise
Wiener Chaos Methods for Linear Stochastic Advection-Diffusion-Reaction Equations
Stochastic Collocation Methods for Differential Equations with White Noise
Comparison Between Wiener Chaos Methods and Stochastic Collocation Methods
Application of Collocation Method to Stochastic Conservation Laws
Part III Spatial White Noise
Semilinear Elliptic Equations with Additive Noise
Multiplicative White Noise: The Wick-Malliavin Approximation
Epilogue
Appendices
A. Basics of Probability
B. Semi-analytical Methods for SPDEs
C. Gauss Quadrature
D. Some Useful Inequalities and Lemmas
E. Computation of Convergence Rate.