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Numerical Differential Equations:
a compact compendium
Roberto De Leo
Contents
Index
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Contents
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Front Matter
Preface
1
Ordinary Differential Equations
Initial Value Problems
Explicit Euler Method
Compensated Summation
Variable step size
Higher Order Methods: Runge-Kutta
Higher Order Methods: Taylor
Higher Order Methods: Multistep
Convergence, Consistency and Stability
Stiff ODEs
Implicit Euler method
Other implicit methods
Euler method in \(\mathbb R^n\)
SciPy's IVP solvers
MATLAB's IVP solvers
Boundary Value Problems
Shooting Method
Finite Differences Method
SciPy's BVP solvers
MATLAB's BVP solvers
Exercises
References and Suggested Readings
2
Partial Differential Equations
General facts about PDEs
Finite Differences Method: Hyperbolic PDEs
Convergence, Consistency and Stability of Finite Difference Methods
Finite Differences Method: Parabolic PDEs
Finite Differences Method: Elliptic PDEs
Finite Elements Method
Spectral Methods
Exercises
References and Suggested Readings
Back Matter
A
Notation
B
GNU Free Documentation License
References and Suggested Readings
Index
Colophon
Authored in PreTeXt
Numerical Differential Equations:
a compact compendium
Roberto De Leo
Department of Mathematics
Howard University
roberto.deleo@howard.edu
January 12, 2023
Preface