using System using System Collections Generic using System Linq using

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using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace RK_methods_diffur
{
class Program
{
static double y(double x)
{
return Math.Pow(Math.E, x);
}
static double p(double x) { return (double)3; }
static double q(double x) { return (double)(-2); }
static double f(double x) { return 2 * y(x); }
static double[] count(int n, double a, double b, double []xi, double []fi)
{
double[] yi = new double[n + 1];
double h = 1 / (double)n;
yi[0] = y(a); yi[n] = y(b);
double[] ai = new double[n];
double[] bi = new double[n];
double[] ci = new double[n];
double[] di = new double[n];
for (int i = 1; i < n; i++)
{
ai[i] = 1.0 - p(xi[i + 1]) * h / 2.0;//1;//
bi[i] = q(xi[i]) * h * h - 2.0;// 4;//
ci[i] = 1.0 + ((p(xi[i]) * h) / 2);//1;//
di[i] = f(xi[i]) * h * h;
}
di[1] -= (1 - p(xi[0]) * h / 2)*yi[0]; di[n - 1] -= (1 + p(xi[n]) * h / 2)*yi[n];//-1.17; //di[2] = di[3] = 6; n = 5;
for (int i = 0; i < n; i++)
Console.WriteLine("a=" + ai[i] + "\tb=" +bi[i]+"\tc="+ci[i]+"\td="+di[i]);
//--------------copy-------------------
double[] alpha = new double[n];
double[] beta = new double[n];
alpha[1] = -ci[1] / bi[1];
beta[1] = di[1] / bi[1];
for (int i = 2; i < n; i++)
{
alpha[i] = -(ci[i] / (ai[i - 1] * alpha[i - 1] + bi[i]));
beta[i] = (di[i] - ai[i - 1] * beta[i - 1]) / (ai[i - 1] * alpha[i - 1] + bi[i]);
}
//for (int i = 1; i < n; i++)
// Console.WriteLine("al="+alpha[i]+"\tbt="+beta[i]);
yi[n-1] = beta[n-1];// (di[n] - ai[n - 1] * beta[n - 1]) / (ai[n - 1] * alpha[n - 1] + bi[n]);
Console.WriteLine("yn: "+ yi[n - 1]);
for (int i = n - 2; i > 0; i--)
yi[i] = alpha[i] * yi[i + 1] + beta[i];
return yi;
}
static void Main(string[] args)
{
int n = 10;
double a = 0, b = 1;
double h = 1 / (double)n;
double []xi = new double[n + 1];
double []yi = new double[n + 1];
double []fi = new double[n + 1];
for (int i = 0; i <= n; i++)
{
double j = a + i * h;
xi[i] = j;
yi[i] = y(j);
fi[i] = f(j);
}
for (int i = 0; i <= n; i++)
Console.WriteLine(xi[i] + "\t" + yi[i] + "\t" + fi[i]);
double []result = count(n, a, b, xi, fi);
result[n] = y(b);
result[0] = y(a);
for (int i = 0; i <= n; i++)
Console.WriteLine("y=" + yi[i] + " \t\tresult=" + result[i] + " d: "+ Math.Abs(yi[i]-result[i]));
//Console.WriteLine("y=" + f(1));
Console.ReadLine();
}
}
}