Numerical Methods for Stochastic Partial Differential Equations with White Noise

1. Prologue
Zhongqiang Zhang, George Em Karniadakis

2. Brownian motion and stochastic calculus
Zhongqiang Zhang, George Em Karniadakis

3. Numerical methods for stochastic differential equations
Zhongqiang Zhang, George Em Karniadakis

Part I. Numerical Stochastic Ordinary Differential Equations

4. Numerical schemes for SDEs with time delay using the Wong-Zakai approximation
Zhongqiang Zhang, George Em Karniadakis

5. Balanced numerical schemes for SDEs with non-Lipschitz coefficients
Zhongqiang Zhang, George Em Karniadakis

Part II. Temporal White Noise

6. Wiener chaos methods for linear stochastic advection-diffusion-reaction equations
Zhongqiang Zhang, George Em Karniadakis

7. Stochastic collocation methods for differential equations with white noise
Zhongqiang Zhang, George Em Karniadakis

8. Comparison between Wiener chaos methods and stochastic collocation methods
Zhongqiang Zhang, George Em Karniadakis

9. Application of collocation method to stochastic conservation laws
Zhongqiang Zhang, George Em Karniadakis

Part III. Spatial White Noise

10. Semilinear elliptic equations with additive noise
Zhongqiang Zhang, George Em Karniadakis

11. Multiplicative white noise: The Wick-Malliavin approximation
Zhongqiang Zhang, George Em Karniadakis

12. Epilogue
Zhongqiang Zhang, George Em Karniadakis

Keywords: Mathematics, Numerical Analysis, Probability Theory and Stochastic Processes, Partial Differential Equations