old_chafen.h

差分法求解微分方程：古典显式法,收敛性最差；古典隐式法；Crank-Nicolson法,收敛性最好

#include <vector>
#include "fn_chafen.h"
#include "math.h"
using namespace std;

vector<double> old_chafen(double a,			//a
						  vector<double> u0,//初始条件
						  vector<double> us,//边界条件
						  vector<double> um,//边界条件
						  double x0,		//x0
						  double t0,		//t0
						  double r,			//a*tao/h/h
						  double tao,		//tao	
						  int total)		//(tn-t0)/tao	
{
	vector<double> u;

	int n = u0.end() - u0.begin();
	for(int i = 0; i < n; i++)
		u.push_back(u0[i]);

	for(int k = 0; k < total - 1; k++)
	{
		u.push_back(us[k]);
		for(i = 0; i < n - 2; i ++)
		{
			double temp;
			temp = (1 - 2 * r) * u[k * n + i + 1] 
				+ r * (u[k * n + i] + u[k * n + i + 2])
				+ tao * fn_chafen((i + 1) * sqrt(tao * a / r) + x0, (k + 1) * tao + t0);
			u.push_back(temp);
		}
		u.push_back(um[k]);
	}
	return u;
}