A9 Ordinary differential equations

Although TScreen provides a perfectly adequate base, additional functionality is again required for displaying graphically the solutions of differential equations, especially when two or more simultaneous equations are involved. In this section we construct the functions required for solving single ordinary differential equations of the form dy/ dx = f( x, y); in the last section we treat two simultaneous equations.

Of course, we must first include the header files:

#include 

and then the definition of the function type:

typedef double(*func)(double, double);

We shall restrict ourselves to Runge-Kutta methods for simplicity ( cf 18.5), although we give ourselves a choice of the order of RK approximation (the technique may easily be extended to include other possibilities). These methods are encapsulated in the class TRKOneDim:

<a name="860"></a><a name="page517"></a>class TRKOneDim {public:      typedef void(TRKOneDim: :*trkf)(func, double,                        double&, double, bool&);      void RK1(func, double, double&, double, bool&);      void RK2(func, double, double&, double, bool&);      void RK4(func, double, double&, double, bool&);};

Notice the appearance of a typedef statement inside the class declaration, and the form that it takes. This allows us to refer to a RK method without initially specifying which one The RK functions are familiar to us from...