This programm solves the differential equation y''(x) - y'(x)/x = -2/x^2^ over the domain [0.5; 1] with boundary conditions y'(0.5) = 0, y(1) = 0. There are three methods implemented and compared:
- order 1 finite difference method
- order 2 finite difference method
- shooting method
The initial value problem in shooting method is solved using the classical 4-order Runge-Kutta method with the following Butcher's table:
| 0 | 0 | 0 | 0 | 0 |
|---|---|---|---|---|
| 1/2 | 1/2 | 0 | 0 | 0 |
| 1/2 | 0 | 1/2 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 |
| --- | 1/6 | 1/3 | 1/3 | 1/6 |
Despite the fact that the programm was written to solve a particular equation, the solver.hpp is still universal for any domain [a;b] and for any two-order differential equation (implying the boundary conditions are y'(a) = yL and y(b) = yR) For other boundary conditions the Shooter::Shoot () method should be changed a little.