The coverage of initial-value methods in section 3.1 is the deepest treatment of numerical ideas in the text;`the concepts of local error, global error, and numerical stability are introduced and analyzed at an appropriate level.
For the finite difference methods of section 9.3, accuracy is explored from two perspectives, the order of the derivative approximations being used and numerical experiments that study the variation in error with mesh size. No complete error analysis is given. The treatment of the methods of lines in section 9.6 is essentially purely formal.
DELab (see section 5 below) provides GUI-based access to the three fixed-step initial-value solvers Euler, Heun, and RK4, as well as MATLAB's adaptive solvers ode23, ode45, ode113 and its stiff solvers ode23s and ode15s. It accommodates systems of arbitrary size, permitting easy solution of the systems of ordinary differential equations generated by the method of lines. As an alternative to direct use of matrix solver commands in the MATLAB command window, it offers simple access to numerical solution of linear algebraic equations to support the use of finite differences.