Contents
1  Some Basics of ODE Integration
1.1  General Initial Value ODE Problem
1.2 Origin of ODE Integrators in the Taylor Series
1.3  The Runge Kutta Method
1.4  Accuracy of RK Methods
1.5  Embedded RK Algorithms
1.6  Library ODE Integrators
1.7  Stability of RK Methods
2  Solution of a 1x1 ODE System
2.1  Programming in MATLAB
2.2  Programming in C
2.3  Programming in C++
2.4  Programming in Fortran
2.5  Programming in Java
2.6  Programming in Maple
3  Solution of a 2x2 ODE System
3.1  Programming in MATLAB
3.2  Programming in C
3.3  Programming in C++
3.4  Programming in Fortran
3.5  Programming in Java
3.6  Programming in Maple
4  Solution of a Linear PDE
4.1  Programming in MATLAB
4.2  Programming in C
4.3  Programming in C++
4.4  Programming in Fortran
4.5  Programming in Java
4.6  Programming in Maple
5  Solution of a Nonlinear PDE
5.1  Programming in MATLAB
5.2  Programming in C
5.3  Programming in C++
5.4  Programming in Fortran

5.5  Programming in Java
5.6  Programming in Maple
AppendixA  Embedded Runge Kutta Pairs
AppendixB  Integrals from ODEs
AppendixC  Stiff ODE Integration
C.1  The BDF Formulas Applied to the 2x2 ODE System
C.2 MATLAB Program for the Solution of the
2x2 ODE System
C.3 MATLAB Program for the Solution of the 2x2 ODE System
Using ode23s and ode15s
AppendixD  Alternative Forms of ODEs
AppendixE  Spatial p Refinement
AppendixF  Testing ODE/PDE Codes