init

2026-01-04 15:35:46 +01:00
commit f53b8768f8
70 changed files with 51910 additions and 0 deletions
--- a/P3/C_DGLSolver.cpp
+++ b/P3/C_DGLSolver.cpp
@@ -0,0 +1,110 @@
+#include "C_DGLSolver.h"
+using namespace std;
+
+C_DGLSolver::C_DGLSolver() {
+}
+
+// Konstruktor für DGL 1. Ordnung
+C_DGLSolver::C_DGLSolver(CMyVektor(*f_DGL_System)(CMyVektor y, double x)) {
+	isDGLSystem = true;
+	fDglSystemZeiger = f_DGL_System;
+}
+
+// Konstruktor für DGL n-ter Ordnung
+C_DGLSolver::C_DGLSolver(double(*f_DGL_nterOrdnung)(CMyVektor y, double x)) {
+	isDGLSystem = false;
+	fDglNterOrdnungZeiger = f_DGL_nterOrdnung;
+}
+
+C_DGLSolver::~C_DGLSolver() {
+}
+
+CMyVektor C_DGLSolver::euler(CMyVektor y, double xStart, double XEnd, double schritte) {
+	double schrittweite = (XEnd - xStart) / schritte;
+	CMyVektor yCopy(y.getDimension());
+	CMyVektor yAbl(y.getDimension());
+	yCopy = y;
+
+	double x = xStart;
+	int s = 0;
+	cout << "h = " << schrittweite << endl;
+
+	for (; s < schritte; s++, x += schrittweite) {
+		yAbl = ableitungen(yCopy, x);
+
+		cout << "Schritt " << s << ": " << endl
+			<< "\t" << " 𝑥 = " << x << endl
+			<< "\t" << " 𝑦 = " << yCopy << endl
+			<< "\t" << "𝑦' = " << yAbl << endl << endl;
+
+		for (int i = 1; i <= yCopy.getDimension(); i++)
+			yCopy.setElement(i, yCopy.getElement(i) + schrittweite * yAbl.getElement(i));
+	}
+
+	cout << "Ende bei " << endl;
+	cout << "\t" << " 𝑥 = " << x << endl;
+	cout << "\t" << " 𝑦 = " << yCopy << endl;
+	return yCopy;
+}
+
+CMyVektor C_DGLSolver::heun(CMyVektor y, double xStart, double XEnd, double schritte) {
+	double schrittweite = (XEnd - xStart) / schritte;
+	CMyVektor yCopy(y.getDimension());
+	CMyVektor yCopyTest(y.getDimension());
+	yCopy = y;
+
+	CMyVektor yAbl(y.getDimension());
+	CMyVektor yAblTest(y.getDimension());
+	CMyVektor fx_mStg(y.getDimension());
+
+	double x = xStart;
+	int s = 0;
+	cout << "h = " << schrittweite << endl;
+
+	for (; s < schritte; x += schrittweite, s++) {
+		yAbl = ableitungen(yCopy, x);
+
+		cout << "Schritt " << s << ": " << endl;
+		cout << "\t" << " 𝑥  = " << x << endl;
+		cout << "\t" << " 𝑦  = " << yCopy << endl;
+
+		cout << "\t" << "𝑦ₒ' = " << yAbl << endl << endl;
+
+
+		for (int i = 1; i <= yCopy.getDimension(); i++)
+			yCopyTest.setElement(i, yCopy.getElement(i) + schrittweite * yAbl.getElement(i));
+
+		yAblTest = ableitungen(yCopyTest, x + schrittweite);
+
+		for (int i = 1; i <= fx_mStg.getDimension(); i++)
+			fx_mStg.setElement(i, 0.5 * (yAbl.getElement(i) + yAblTest.getElement(i)));
+
+		for (int i = 1; i <= yCopy.getDimension(); i++)
+			yCopy.setElement(i, yCopy.getElement(i) + schrittweite * fx_mStg.getElement(i));
+
+		cout << "\t" << " 𝑦ₜ = " << yCopyTest << endl;
+		cout << "\t" << "𝑦ₜ' = " << yAblTest << endl << endl;
+		cout << "\t" << "𝑦ₘ' = " << fx_mStg << endl << endl;
+	}
+
+	cout << "Ende bei " << endl
+		<< "\t" << " 𝑥  = " << x << endl
+		<< "\t" << " 𝑦  = " << yCopy << endl;
+
+	return yCopy;
+}
+
+CMyVektor C_DGLSolver::ableitungen(CMyVektor y, double x) {
+	CMyVektor result(y.getDimension());
+
+	if (isDGLSystem) {
+		result = fDglSystemZeiger(y, x);
+	}
+	else {
+		for (int i = 1; i < y.getDimension(); i++)
+			result.setElement(i, y.getElement(i + 1));
+			
+		result.setElement(y.getDimension(), fDglNterOrdnungZeiger(y, x));
+	}
+	return result;
+}