Finite Difference Methods for Ordinary and Partial Differential Equations

Randall J. LeVeque is a Professor in the Departments of Mathematics and Applied Mathematics at the University of Washington, Seattle.

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.