/*
* Provides grid that is analysis of GTE for different number of grid cells
* Analysis n from nStart to nFinish
*/
public Grid GTEAnalysisGrid(int nStart, int nFinish)
{
// grid to fill in
Grid grid = new Grid(nStart, nFinish);
// enumerate ovel all n
for (int n = nStart; n <= nFinish; n++)
{
// construct exact solution grid with given number of steps
MyExactSolution myExactSolutionGrid = new MyExactSolution(n, x[0], y[0], x[N]);
// compute numerical method approximation for the given n
double[] yNumerical = ComputeValues(myExactSolutionGrid.x, y[0]);
double[] yExact = myExactSolutionGrid.y;
// find maximum error in the grid
grid.y[n - nStart] = Math.Abs(yNumerical[0] - yExact[0]);
for (int i = 1; i <= n; i++)
{
grid.y[n - nStart] = Math.Max(grid.y[n - nStart], Math.Abs(yNumerical[i] - yExact[i]));
}
}
// return GTE analysis grid for plotting
return(grid);
}
/*
* Function to redraw charts based on the provided parameters by the user.
* Triggers when button plot&analyze is clicked.
*/
private void buttonIVPPlotClick(object sender, EventArgs e)
{
try
{
// collect data from text boxes on this tab
double x0 = Double.Parse(textBoxx0.Text); // x0 - initial value of x
double y0 = Double.Parse(textBoxy0.Text); // y0 - initial value of y
double X = Double.Parse(textBoxX.Text); // X - right border of the interval
int N = Int32.Parse(textBoxN.Text); // N - number of grid cells
// data is collected
int nStart = Int32.Parse(textBoxnStart.Text); // nStart - left border for GTEAnalysis
int nFinish = Int32.Parse(textBoxnFinish.Text); // nFinish - right border for GTEAnalysis
// Solve IVP for each method and bind data to the charts so it will be plotted
// Euler Method solution grid
EulerMethod EulerGrid = new EulerMethod(N, x0, y0, X, new MyFunction());
chartIVP.Series["Euler"].Points.DataBindXY(EulerGrid.x, EulerGrid.y);
// Improved Euler method solution grid
ImprovedEulerMethod ImprovedEulerGrid =
new ImprovedEulerMethod(N, x0, y0, X, new MyFunction());
chartIVP.Series["ImprovedEuler"].Points.DataBindXY(ImprovedEulerGrid.x, ImprovedEulerGrid.y);
// Runge Kutta method solution grid
RungeKuttaMethod RungeKuttaGrid =
new RungeKuttaMethod(N, x0, y0, X, new MyFunction());
chartIVP.Series["RungeKutta"].Points.DataBindXY(RungeKuttaGrid.x, RungeKuttaGrid.y);
// Exact solution grid
MyExactSolution myExactSolutionGrid = new MyExactSolution(N, x0, y0, X);
chartIVP.Series["Exact"].Points.DataBindXY(myExactSolutionGrid.x, myExactSolutionGrid.y);
// set limits on x-axis for charts
// Initial Value Problem chart
chartIVP.ChartAreas[0].AxisX.Minimum = x0;
chartIVP.ChartAreas[0].AxisX.Maximum = X;
// LTE analysis chart
chartLTE.ChartAreas[0].AxisX.Minimum = x0;
chartLTE.ChartAreas[0].AxisX.Maximum = X;
// GTE analysis chart
chartEA.ChartAreas[0].AxisX.Minimum = nStart;
chartEA.ChartAreas[0].AxisX.Maximum = nFinish;
// Compute LTE for each method and bind data to the charts so it will be plotted
// LTE for Euler method grid
Grid LTEEuler = EulerGrid.LTEGrid(myExactSolutionGrid);
chartLTE.Series["Euler"].Points.DataBindXY(LTEEuler.x, LTEEuler.y);
// LTE for Improved Euler method grid
Grid LTEImprovedEuler = ImprovedEulerGrid.LTEGrid(myExactSolutionGrid);
chartLTE.Series["ImprovedEuler"].Points.DataBindXY(LTEImprovedEuler.x, LTEImprovedEuler.y);
// LTE for Runge Kutta method grid
Grid LTERungeKutta = RungeKuttaGrid.LTEGrid(myExactSolutionGrid);
chartLTE.Series["RungeKutta"].Points.DataBindXY(LTERungeKutta.x, LTERungeKutta.y);
// Compute GTE for each method and bind data to the charts so it will be plotted
// GTE Euler method analysis grid
Grid GTEEuler = EulerGrid.GTEAnalysisGrid(nStart, nFinish);
chartEA.Series["Euler"].Points.DataBindXY(GTEEuler.x, GTEEuler.y);
// GTE Improved Euler method analysis grid
Grid GTEImprovedEuler = ImprovedEulerGrid.GTEAnalysisGrid(nStart, nFinish);
chartEA.Series["ImprovedEuler"].Points.DataBindXY(GTEImprovedEuler.x, GTEImprovedEuler.y);
// GTE Runge Kutta method analysis grid
Grid GTERungeKutta = RungeKuttaGrid.GTEAnalysisGrid(nStart, nFinish);
chartEA.Series["RungeKutta"].Points.DataBindXY(GTERungeKutta.x, GTERungeKutta.y);
}
catch
{
}
}