kursovaya

#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <fstream>
#include <vector>
#include <algorithm>
#include <string>
#include <conio.h>
using namespace std;

vector<double> DL, D, DR;
double hx;

double Func(double x)
{
	return -12*x*x;
}

double UFunc(double x)
{
	return x*x*x*x;
}

vector<vector<double>> LocalG(double L)
{
	const double G1[2][2] = {
			{  1,  -1},
			{ -1,  1} };
	vector<vector<double>> G2;
	G2.resize(2);
	for (int i = 0; i < 2; i++)
		G2[i].resize(2);
	for (int i = 0; i < 2; i++)
	{
		for (int j = 0; j < 2; j++)
		{
			G2[i][j] = G1[i][j] * L / hx;
		}
	}
	return G2;
}

void GlobalG(double L, const  vector<double >& x)
{
	int size = x.size();
	vector<vector<double>> G = LocalG(L);
	for (int i = 0; i < size - 1; i++)
	{
		D[i] += G[0][0];
		D[i + 1] += G[1][1];
		DL[i + 1] += G[0][1];
		DR[i] += G[1][0];
	}
}

vector<double> Mult(vector<vector<double>>& m, vector<double>& v)
{
	vector<double> out;
	out.resize(2);
	for (int i = 0; i < 2; i++)
	{
		out[i] = 0;
		for (int j = 0; j < 2; j++)
			out[i] += m[i][j] * v[j];
	}
	return out;
}

vector<vector<double>> LocalM(double koef)
{
	const double m[2][2] =
	{
			{2, 1 },
			{1, 2}
	};
	vector<vector<double>> M;
	M.resize(2);
	for (int i = 0, size = M.size(); i < size; ++i)
		M[i].resize(2);
	for (int i = 0; i < 2; i++)
	{
		for (int j = 0; j < 2; j++)
		{
			M[i][j] = koef * hx * m[i][j] / 6;
		}
	}
	return M;
}

vector<double> GlobalF(double G, const vector<double >& x)
{
	int countOfElements = (x.size() - 1);
	vector<double> F;
	F.resize(x.size());
	for (int k = 0; k < countOfElements; ++k)
	{
		vector<vector<double>> tmp = LocalM(G);
		vector<double> F1;
		F1.resize(2);
		F1[0] = Func(x[k]);
		F1[1] = Func(x[k + 1]);
		F1 = Mult(tmp, F1);
		F[k] += F1[0];
		F[k + 1] += F1[1];
	}
	return F;
}

vector<double> Compute(int& size, vector<double>& s)
{
	vector<double> U;
	U.resize(size);
	for (int i = 0; i < size - 1; i++)
	{
		if (D[i] != 0)
		{
			double K1 = -DL[i + 1] / D[i];
			DL[i + 1] = 0;
			D[i + 1] += K1 * DR[i];
			s[i + 1] += K1 * s[i];
		}
	}
	U[size - 1] = s[size - 1] / D[size - 1];
	for (int i = size - 2; i > -1; i--)
	{
		U[i] = (s[i] - DR[i] * U[i + 1]) / D[i];
	}
	return U;
}

void FBC(int size, vector<double>& v, double kraev1, double kraev2)
{
	D[0] = 1;
	DR[0] = 0;
	v[0] = kraev1;
	D[size - 1] = 1;
	DL[size - 1] = 0;
	v[size - 1] = kraev2;
}

int main()
{
	setlocale(LC_ALL, "Russian");
	double L = 0, G = 0, kraev1 = 0, kraev2 = 0;
	FILE* fin;
	fin = fopen("lyambda.txt", "r");
	fscanf(fin, "%lf", &L);
	fin = fopen("gamma.txt", "r");
	fscanf(fin, "%lf", &G);
	int kol_el = 0;
	double tmp = 0, tmp1 = 0;
	int tmp2 = 0;
	vector<double> x;
	fin = fopen("x.txt", "r");
	fscanf(fin, "%lf", &tmp);
	fscanf(fin, "%lf", &tmp1);
	fscanf(fin, "%d", &tmp2);
	fclose(fin);
	hx = (tmp1 - tmp) / tmp2;
	for (int i = 0; i <= tmp2; i++) x.emplace_back(tmp + i * hx);
	kraev1 = UFunc(x[0]);
	kraev2 = UFunc(x[tmp2]);
	int size = x.size();
	DL.resize(size);
	D.resize(size);
	DR.resize(size);
	GlobalG(L, x);
	vector<double> F = GlobalF(G, x);
	FBC(size, F, kraev1, kraev2);
	vector<double> u = Compute(size, F);
	FILE* fout;
	fout = fopen("U.txt", "w");
	fprintf(fout, "x				u				u*					|u-u*|			|u-u*/u*|	\n");
	for (int i = 0; i < size; i++)
	{
		fprintf(fout, "%lf		%lf		%lf		%lf		%lf	\n", x[i], u[i], UFunc(x[i]), abs(u[i] - UFunc(x[i])), abs((u[i] - UFunc(x[i])) / UFunc(x[i])));
	}
	return 0;
}