Finite Difference Methods for Ordinary and Partial Differential Equations - Randall J Leveque

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Résumé :

• Preface
• Part I: Boundary Value Problems and Iterative Methods.
• Chapter 1: Finite Difference Approximations
• Chapter 2: Steady States and Boundary Value Problems
• Chapter 3: Elliptic Equations
• Chapter 4: Iterative Methods for Sparse Linear Systems
• Part II: Initial Value Problems.
• Chapter 5: The Initial Value Problem for Ordinary Differential Equations
• Chapter 6: Zero-Stability and Convergence for Initial Value Problems
• Chapter 7: Absolute Stability for Ordinary Differential Equations
• Chapter 8: Stiff Ordinary Differential Equations
• Chapter 9: Diffusion Equations and Parabolic Problems
• Chapter 10: Advection Equations and Hyperbolic Systems
• Chapter 11: Mixed Equations
• Appendix A: Measuring Errors
• Appendix B: Polynomial Interpolation and Orthogonal Polynomials
• Appendix C: Eigenvalues and Inner-Product Norms
• Appendix D: Matrix Powers and Exponentials
• Appendix E: Partial Differential Equations
• Bibliography
• Index.