old_y_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>
using namespace std;

#include "math.h"
#include "zhuigang.h"


vector<double> old_y_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, utemp;

	int n = u0.end() - u0.begin();
	
	vector<double> aa, b, c, d;

	for(int i = 0; i < n - 3; i++)
	{
		aa.push_back(- r);
		c.push_back(- r);
	}

	for(i = 0; i < n - 2; i++)
	{
		b.push_back(1 + r * 2);
		d.push_back(0);
	}
	

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


	for(int k = 0; k < total - 1; k++)
	{
		u.push_back(us[k]);


		d[0] = tao * fn_chafen(sqrt(tao * a / r) + x0, t0 + (k + 1) * tao)
			+ r * arpha(t0 + (k + 1) * tao)
			+ u[k * n + 1];
		for(i = 1; i < n - 3; i++)
		{
			d[i] = tao * fn_chafen(sqrt(tao * a / r) * (i) + x0, t0 + (k + 1) * tao)
				+ u[k * n + i + 1];
		}
		d[n - 3] = tao * fn_chafen(sqrt(tao * a / r) * (n - 3) + x0, t0 + (k + 1) * tao)
			+ r * beta(t0 + (k + 1) * tao)
			+ u[k * n + n - 2];

		utemp = zhuigang(aa, b, c, d);

		
		for(i = 0; i < n - 2; i++)
			u.push_back(utemp[n - 3 - i]);

		u.push_back(um[k]);
	}

	return u;
}