public List <Tuple <double, double> > getMaxError(double X0, double Y0, double UPPER_BOUND, int num_segments, int method)
{
List <Tuple <double, double> > Points = new List <Tuple <double, double> >();
for (int i = 1; i <= num_segments; i++)
{
List <Tuple <double, double> > PointsOfMethod = new List <Tuple <double, double> >();
List <Tuple <double, double> > Solution = new List <Tuple <double, double> >();
if (method == 1)
{
PointsOfMethod = euler.solve(X0, Y0, UPPER_BOUND, i);
}
else if (method == 2)
{
PointsOfMethod = improved_euler.solve(X0, Y0, UPPER_BOUND, i);
}
else
{
PointsOfMethod = runge_kutta.solve(X0, Y0, UPPER_BOUND, i);
}
Points.Add(Tuple.Create((double)i, getMax(PointsOfMethod)));
}
return(Points);
}
public void drawPlot(Chart chart1, double X0, double Y0, double UPPER_BOUND, int num_segments, int method)
{
List <Tuple <double, double> > ApproxSolutionPoints1 = new List <Tuple <double, double> >();
List <Tuple <double, double> > ApproxSolutionPoints2 = new List <Tuple <double, double> >();
List <Tuple <double, double> > ApproxSolutionPoints3 = new List <Tuple <double, double> >();
MyEquation equation = new MyEquation();
Euler euler = new Euler();
ImprovedEuler improved_euler = new ImprovedEuler();
RungeKutta runge_kutta = new RungeKutta();
if (method == 1)
{
ApproxSolutionPoints1 = euler.solve(X0, Y0, UPPER_BOUND, num_segments);
for (int i = 0; i <= num_segments; i++)
{
double localError = Math.Abs(ApproxSolutionPoints1.ElementAt(i).Item2 - equation.exactSolution(ApproxSolutionPoints1.ElementAt(i).Item1));
chart1.Series[0].Points.AddXY(ApproxSolutionPoints1.ElementAt(i).Item1, localError);
}
chart1.Series[0].IsVisibleInLegend = true;
chart1.Series[0].Name = "Euler's\nmethod";
}
else if (method == 2)
{
ApproxSolutionPoints1 = improved_euler.solve(X0, Y0, UPPER_BOUND, num_segments);
for (int i = 0; i <= num_segments; i++)
{
double localError = Math.Abs(ApproxSolutionPoints1.ElementAt(i).Item2 - equation.exactSolution(ApproxSolutionPoints1.ElementAt(i).Item1));
chart1.Series[0].Points.AddXY(ApproxSolutionPoints1.ElementAt(i).Item1, localError);
}
chart1.Series[0].IsVisibleInLegend = true;
chart1.Series[0].Name = "Improved Euler's\nmethod";
}
else if (method == 3)
{
ApproxSolutionPoints1 = runge_kutta.solve(X0, Y0, UPPER_BOUND, num_segments);
for (int i = 0; i <= num_segments; i++)
{
double localError = Math.Abs(ApproxSolutionPoints1.ElementAt(i).Item2 - equation.exactSolution(ApproxSolutionPoints1.ElementAt(i).Item1));
chart1.Series[0].Points.AddXY(ApproxSolutionPoints1.ElementAt(i).Item1, localError);
}
chart1.Series[0].IsVisibleInLegend = true;
chart1.Series[0].Name = "Runge-Kutta\nmethod";
}
else
{
ApproxSolutionPoints1 = euler.solve(X0, Y0, UPPER_BOUND, num_segments);
ApproxSolutionPoints2 = improved_euler.solve(X0, Y0, UPPER_BOUND, num_segments);
ApproxSolutionPoints3 = runge_kutta.solve(X0, Y0, UPPER_BOUND, num_segments);
for (int i = 0; i <= num_segments; i++)
{
double localError = Math.Abs(ApproxSolutionPoints1.ElementAt(i).Item2 - equation.exactSolution(ApproxSolutionPoints1.ElementAt(i).Item1));
chart1.Series[0].Points.AddXY(ApproxSolutionPoints1.ElementAt(i).Item1, localError);
}
for (int i = 0; i <= num_segments; i++)
{
double localError = Math.Abs(ApproxSolutionPoints2.ElementAt(i).Item2 - equation.exactSolution(ApproxSolutionPoints2.ElementAt(i).Item1));
chart1.Series[1].Points.AddXY(ApproxSolutionPoints2.ElementAt(i).Item1, localError);
}
for (int i = 0; i <= num_segments; i++)
{
double localError = Math.Abs(ApproxSolutionPoints3.ElementAt(i).Item2 - equation.exactSolution(ApproxSolutionPoints3.ElementAt(i).Item1));
chart1.Series[2].Points.AddXY(ApproxSolutionPoints3.ElementAt(i).Item1, localError);
}
chart1.Series[0].IsVisibleInLegend = true;
chart1.Series[1].IsVisibleInLegend = true;
chart1.Series[2].IsVisibleInLegend = true;
chart1.Series[0].Name = "Euler's\nmethod";
chart1.Series[1].Name = "Improved Euler's\nmethod";
chart1.Series[2].Name = "Runge-Kutta\nmethod";
}
// Design of charts
chart1.ChartAreas[0].AxisX.LabelStyle.Format = "0.00";
chart1.ChartAreas[0].AxisX.MajorGrid.LineColor = Color.LightGray;
chart1.ChartAreas[0].AxisY.MajorGrid.LineColor = Color.LightGray;
}