internal override List <PointD>[] Solve(double x0, double y0, double max, int num, int max_er)
{
double h = (max - x0) / num; //step size
PointD point = new PointD();
Exact exacEquation = new Exact();
List <PointD>[] result = new List <PointD> [3]; //creating a list
result[0] = new List <PointD>(); // List for points of Euler's method grapgh
result[1] = new List <PointD>(); // List for local errors of the Euler's method
result[2] = new List <PointD>(); // List for global error plotting
double x = x0, y = y0;
while (x <= max) //Euler's method
{
point.X = x;
point.Y = y;
result[0].Add(point);
double localError = Math.Abs(y - exacEquation.getValue(x, x0, y0));
point.X = x;
point.Y = localError;
result[1].Add(point);
double k1 = orig(x, y);
double k2 = orig(x + h / 2, y + h * k1 / 2);
double k3 = orig(x + h / 2, y + h * k2 / 2);
double k4 = orig(x + h, y + h * k3);
y = y + h * (k1 + 2 * k2 + 2 * k3 + k4) / 6;
x = x + h;
}
//global error
for (int i = 0; i < max_er; i++)
{
x = x0;
y = y0;
h = (max - x0) / (i + 1);
for (int j = 0; j < i + 1; j++)
{
double k1 = orig(x, y);
double k2 = orig(x + h / 2, y + h * k1 / 2);
double k3 = orig(x + h / 2, y + h * k2 / 2);
double k4 = orig(x + h, y + h * k3);
y = y + h * (k1 + 2 * k2 + 2 * k3 + k4) / 6;
x = x + h;
}
if (i > 1)
{
double globalError = Math.Abs(y - exacEquation.getValue(x, x0, y0));
point.X = i;
point.Y = globalError;
result[2].Add(point);
}
}
return(result);
}
private void buttonCalculate_Click(object sender, EventArgs e)
{
Chart1.Series.Clear();
Chart2.Series.Clear();
Chart3.Series.Clear();
double x0 = Double.Parse(textBoxX0.Text);
double y0 = Double.Parse(textBoxY0.Text);
double max = Double.Parse(textBoxX.Text);
int num = int.Parse(textBoxSteps.Text);
int max_err = int.Parse(textBoxIntervalFrom.Text);
SeriesCollection[] series = new SeriesCollection[3];
for (int i = 0; i < 3; i++)
{
series[i] = new SeriesCollection();
}
ChartValues <ObservablePoint>[] values = new ChartValues <ObservablePoint> [10];
for (int i = 0; i < 10; i++)
{
values[i] = new ChartValues <ObservablePoint>();
}
List <PointD> exact = Exact.Solve(x0, y0, max, num);
foreach (var value in exact)
{
values[0].Add(new ObservablePoint(value.X, value.Y));
}
series[0].Add(new LiveCharts.Wpf.LineSeries()
{
Title = "Exact", Values = values[0], PointGeometrySize = 0
});
List <PointD>[] result_euler = (new Euler()).Solve(x0, y0, max, num, max_err);
foreach (var value in result_euler[0])
{
values[1].Add(new ObservablePoint(value.X, value.Y));
}
series[0].Add(new LiveCharts.Wpf.LineSeries()
{
Title = "Euler", Values = values[1], PointGeometrySize = 0
});
List <PointD>[] result_ext = (new Euler_ex()).Solve(x0, y0, max, num, max_err);
foreach (var value in result_ext[0])
{
values[2].Add(new ObservablePoint(value.X, value.Y));
}
series[0].Add(new LiveCharts.Wpf.LineSeries()
{
Title = "Euler_ex", Values = values[2], PointGeometrySize = 0
});
List <PointD>[] result_ru = (new Runge_Kutta()).Solve(x0, y0, max, num, max_err);
foreach (var value in result_ru[0])
{
values[3].Add(new ObservablePoint(value.X, value.Y));
}
series[0].Add(new LiveCharts.Wpf.LineSeries()
{
Title = "Runge_Kutta", Values = values[3], PointGeometrySize = 0
});
Chart1.Series = series[0];
foreach (var value in result_euler[1])
{
values[4].Add(new ObservablePoint(value.X, value.Y));
}
series[1].Add(new LiveCharts.Wpf.LineSeries()
{
Title = "Euler", Values = values[4], PointGeometrySize = 0
});
foreach (var value in result_ext[1])
{
values[5].Add(new ObservablePoint(value.X, value.Y));
}
series[1].Add(new LiveCharts.Wpf.LineSeries()
{
Title = "Euler_ex", Values = values[5], PointGeometrySize = 0
});
foreach (var value in result_ru[1])
{
values[6].Add(new ObservablePoint(value.X, value.Y));
}
series[1].Add(new LiveCharts.Wpf.LineSeries()
{
Title = "Runge_Kutta", Values = values[6], PointGeometrySize = 0
});
Chart2.Series = series[1];
foreach (var value in result_euler[2])
{
values[7].Add(new ObservablePoint(value.X, value.Y));
}
series[2].Add(new LiveCharts.Wpf.LineSeries()
{
Title = "Euler", Values = values[7], PointGeometrySize = 0
});
foreach (var value in result_ext[2])
{
values[8].Add(new ObservablePoint(value.X, value.Y));
}
series[2].Add(new LiveCharts.Wpf.LineSeries()
{
Title = "Euler_ex", Values = values[8], PointGeometrySize = 0
});
foreach (var value in result_ru[2])
{
values[9].Add(new ObservablePoint(value.X, value.Y));
}
series[2].Add(new LiveCharts.Wpf.LineSeries()
{
Title = "Runge_Kutta", Values = values[9], PointGeometrySize = 0
});
Chart3.Series = series[2];
}