double RungeKuttaSolver::SolveEquation()
{
double h = GetStepSize();
double t_previous = GetInitialTime();
double t1 = GetFinalTime();
double y_previous = getInitialValue();
double y_current = getInitialValue();
double k1, k2, k3, k4;
while (t_previous + h < t1)
{
k1 = h * RightHandSide(y_previous, t_previous);
k2 = h * RightHandSide(y_previous + 0.5 * k1, t_previous + 0.5 * h);
k3 = h * RightHandSide(y_previous + 0.5 * k2, t_previous + 0.5 * h);
k4 = h * RightHandSide(y_previous + k3, t_previous + h);
y_current = y_previous + (1.0 / 6.0) * (k1 + 2 * k2 + 2 * k3 + k4);
t_previous += h;
y_previous = y_current;
}
return y_current;
}
double* ForwardEulerSolver::SolveEquation(){
double* output = new double[GetIterationNumber()];
double y = GetInitialValue();
output[0] = y;
for (int i = 1; i < GetIterationNumber(); ++i) {
output[i] = y + GetStepSize()*RightHandSide(y, GetInitialTime() + i*GetStepSize());
y = output[i];
}
return output;
}
void RungeKuttaSolver::SolveEquation(std::ostream& stream)
{
double y = GetInitialValue();
double t = GetInitialTime();
double h = GetStepSize();
assert(h > 1e-6);
std::cout << "Step size: " << h << std::endl;
int n = static_cast<int>(
std::floor((GetFinalTime() - GetInitialTime()) / h));
stream << t << " " << y << "\n";
for (int i = 1; i <= n; ++i) {
double k1 = h * RightHandSide(y, t);
double k2 = h * RightHandSide(y + 0.5 * k1, t + 0.5 * h);
double k3 = h * RightHandSide(y + 0.5 * k2, t + 0.5 * h);
double k4 = h * RightHandSide(y + k3, t + h);
double temp = y + 1.0/6.0 * (k1 + 2 * k2 + 2 * k3 + k4);
if (-1e-6 <= temp && temp <= 0.0) {
y = 0.0;
} else if (1.0 <= temp && temp <= (1.0 + 1e-6) ) {
y = 1.0;
} else if (0.0 < temp && temp < 1.0) {
y = temp;
} else {
// Freak out!
throw Exception("STEP", "Step size too large.");
}
t += h;
stream << t << " " << y << "\n";
}
}
ForwardEulerSolver::ForwardEulerSolver(int N, double startTime, double endTime, double initialValue){
if (endTime > startTime){
if (N > 1){
SetIterationNumber(N);
SetInitialValue(initialValue);
SetTimeInterval(startTime, endTime);
SetStepSize((endTime - startTime)/(N - 1));
double* output = SolveEquation();
for (int i = 0; i < GetIterationNumber(); ++i) {
std::cout << output[i] << " " << GetInitialTime() + i*GetStepSize() << " " << test(GetInitialTime() + i*GetStepSize())<< "\n";
}
}
else{
std::cerr << "The number of iterations needs to be > 1!!\n";
}
}
else{
std::cerr << "Final time needs to be after initial!!\n";
}
}
