// Update chart of LTEs.
public void UpdateChartLTE(DifferentialEquation MyDifferentialEquation, Euler EulerApproximation, ImprovedEuler ImprovedEulerApproximation, RungeKutta RungeKuttaApproximation, double X0, double X)
{
// Set minimum and maximum values of Tab1ChartLTE.
Tab1ChartLTE.ChartAreas[0].AxisX.Minimum = X0;
Tab1ChartLTE.ChartAreas[0].AxisX.Maximum = X;
// Plot the graphs of Local Truncation errors of numerical solutions.
Tab1ChartLTE.Series[0].Points.DataBindXY(EulerApproximation.GetX(), EulerApproximation.ComputeLocalTruncationErrors(MyDifferentialEquation));
Tab1ChartLTE.Series[1].Points.DataBindXY(ImprovedEulerApproximation.GetX(), ImprovedEulerApproximation.ComputeLocalTruncationErrors(MyDifferentialEquation));
Tab1ChartLTE.Series[2].Points.DataBindXY(RungeKuttaApproximation.GetX(), RungeKuttaApproximation.ComputeLocalTruncationErrors(MyDifferentialEquation));
}
// 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());
}
/* Method calculating point-wise approximation. Implementation of the Runge-Kutta Method.
* Returns an approximation at a point with given index i.
*/
public override double ComputeForPoint(double[] x, double[] y, int i, DifferentialEquation MyDifferentialEquation)
{
// Initialize temporary variables.
double h = GetStep(), K1, K2, K3, K4;
// By default use RK4.
K1 = MyDifferentialEquation.Derivative(x[i], y[i]);
K2 = MyDifferentialEquation.Derivative(x[i] + h / 2, y[i] + h / 2 * K1);
K3 = MyDifferentialEquation.Derivative(x[i] + h / 2, y[i] + h / 2 * K2);
K4 = MyDifferentialEquation.Derivative(x[i] + h, y[i] + h * K3);
return(y[i] + h / 6 * (K1 + 2 * K2 + 2 * K3 + K4));
}
/* 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);
}
/* Method solving given ordinary differential equation MyDifferentialEquation.
* Returns y-coordinates of an solution approximation.
*/
public double[] Apply(DifferentialEquation MyDifferentialEquation)
{
// Get number of grid steps.
int N = GetN();
// Get values of x-coordinates.
double[] x = GetX();
// Get values of y-coordinates.
double[] y = GetY();
// Iteratively compute an approximation for each grid step.
for (int i = 1; i < N; i++)
{
y[i] = ComputeForPoint(x, y, i - 1, MyDifferentialEquation);
// Debug information.
// System.Diagnostics.Debug.WriteLine("y[i]={0:F} | x[i - 1]={1:F} y[i - 1]={2:F} h={3:F} Derivative={4:f}", y[i], x[i - 1], y[i - 1], GetStep(), MyDifferentialEquation.Derivative(x[i - 1], y[i - 1]));
}
// Set y-coordinates.
SetY(y);
return(y);
}
/* Method calculating point-wise approximation. Implementation of the Euler Method. * Returns an approximation at a point with given index i. */ public override double ComputeForPoint(double[] x, double[] y, int i, DifferentialEquation MyDifferentialEquation) => y[i] + (GetStep() * MyDifferentialEquation.Derivative(x[i], y[i]));
// Request replotting graphs on chart for GTEs.
public void RequestUpdateChartGTE(DifferentialEquation MyDifferentialEquation,
Euler EulerApproximation,
ImprovedEuler ImprovedEulerApproximation,
RungeKutta RungeKuttaApproximation,
double X0,
double X) => NewView.UpdateChartGTE(MyDifferentialEquation, EulerApproximation, ImprovedEulerApproximation, RungeKuttaApproximation, X0, X);
/* Default implementation of a method calculating point-wise approximation. * Unique for each Numerical method. * Returns approximation at a point with given index i. */ public virtual double ComputeForPoint(double[] x, double[] y, int i, DifferentialEquation MyDifferentialEquation) => 0;