/* Method computing Global Truncation Errors of Numerical Method.
* Apply() should be called before utilizing this method.
* Returns array of GTE's at every point of grid.
*/
public double[] ComputeGlobalTruncationErrors(DifferentialEquation MyDifferentialEquation)
{
// Get exact values of y-coordinates.
double[] y = GetY();
// Initialize an array to store Global Truncation errors.
double[] GTE = new double[GetN()];
// Iteratively compute Global Truncation error for each grid step.
for (int i = 0; i < GetN(); i++)
{
GTE[i] = Math.Abs(y[i] - MyDifferentialEquation.GetY()[i]);
}
return(GTE);
}
/* Method computing Local Truncation Errors of Numerical Method.
* Apply() should be called before utilizing this method.
* Returns array of LTE's at every point of grid.
*/
public double[] ComputeLocalTruncationErrors(DifferentialEquation MyDifferentialEquation)
{
// Get values of x-coordinates.
double[] x = GetX();
// Get exact values of y-coordinates.
double[] y = MyDifferentialEquation.GetY();
// Initialize an array to store Local Truncation errors.
double[] LTE = new double[GetN()];
// Local Truncation error for a first point is 0 as it given by IVP.
LTE[0] = 0;
// Iteratively compute Local Truncation error for each grid step.
for (int i = 1; i < GetN(); i++)
{
LTE[i] = Math.Abs(ComputeForPoint(x, y, i - 1, MyDifferentialEquation) - y[i]);
}
return(LTE);
}
// Update chart of approximations.
public void UpdateChartApproximation(DifferentialEquation MyDifferentialEquation, Euler EulerApproximation, ImprovedEuler ImprovedEulerApproximation, RungeKutta RungeKuttaApproximation, double X0, double X)
{
// Set minimum and maximum values of Tab1ChartApproximation.
Tab1ChartApproximation.ChartAreas[0].AxisX.Minimum = X0;
Tab1ChartApproximation.ChartAreas[0].AxisX.Maximum = X;
// Plot the graphs of exact and numerical solutions.
Tab1ChartApproximation.Series[0].Points.DataBindXY(MyDifferentialEquation.GetX(), MyDifferentialEquation.GetY());
Tab1ChartApproximation.Series[1].Points.DataBindXY(EulerApproximation.GetX(), EulerApproximation.GetY());
Tab1ChartApproximation.Series[2].Points.DataBindXY(ImprovedEulerApproximation.GetX(), ImprovedEulerApproximation.GetY());
Tab1ChartApproximation.Series[3].Points.DataBindXY(RungeKuttaApproximation.GetX(), RungeKuttaApproximation.GetY());
}