35.1 Encapsulating Differential Equations (.NET, C#, CSharp, VB, Visual Basic, F#)
Class FirstOrderInitialValueProblem
represents a first order initial value differential equation. If 
is the unknown
function, the first order initial value problem may be stated as
where 
denotes the first derivative of y
with respect to x, F
is a continuous function with bounded partial derivatives, and 
is the value of
the unknown function y at the point
.
A FirstOrderInitialValueProblem
instance is constructed from a function, F,
and initial value, 
and 
.
The function F is encapsulated as
a Func<double, double, double>, a
delegate which takes two doubles and returns a double.
For example, the following code constructs a FirstOrderInitialValueProblem where 
:
Code Example – C# ordinary differential equations (ODE)
Func<double, double, double> f =
delegate( double x, double y )
{
return x * x;
};
double x0 = 0.0;
double y0 = 1.0;
FirstOrderInitialValueProblem prob =
new FirstOrderInitialValueProblem( f, x0, y0 );