Chapter 1 Introduction 1
Chapter 2 Brief Introduction of Markov Chain and Nonnegative Matrices 6
Chapter 3 The Methods of Solving Elliptic Boundary Value Problem 12
3.1 Elliptic Boundary Value Prollem and Limit Transfer Matrix Q∞ 12
3.2 Method of Solving Nonhomogeneous Elliptic Boundary Value Problem 15
3.3 Solving Parabolic Problem 17
3.4 Monte-Carlo Method of Computing Q∞ and S∞ 19
3.5 Methods of Fast Approximate to limit Matrices Q∞ and S∞ 22
3.6 Under the Case That P Is Not Nonnegative Matrix 24
3.7 Iterative Method for Finite Element Probability Computing 26
Chapter 4 The Finite Element Probability Computing Method 28
Chapter 5 High Accuracy Methods of Finite Element Probability Computing Method 35
5.1 The Probability Multigrid Method 35
5.2 The Boundary Thickening Method 41
5.3 Numerical Experiment 42
Chapter 6 Rectangular Finite Element Probability Computing Method 45
6.1 Introduction 45
6.2 Probability Computing Model and Its Convergence Conditions 46
6.3 Numerical Experiment 50
Chapter 7 Dimentional Independence 52
Chapter 8 The Fast Computing Scheme of the Finite Element Method for the Two Point Boundary Problem 57
8.1 Model Problem and P'k-type Finite Element Space 57
8.2 The Probability Computing Scheme 62
8.3 Numerical Experiment 65
Chapter 9 Example Analysis 67
9.1 The Monte-Carlo Method for Three-dimensional Problems 67
9.2 The Finite Element Monte-Carlo Method of Plate Problems 69
Chapter 10 The Space Decomposition Method of the Finite Element 75
10.1 Abstract Problem 75
10.2 The Domain Decomposition Method and the Structure of Space ？0 81
10.3 Example 83
10.4 Probability Computing Method 85
References 87