newtonraphson.h

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#ifndef NEWTONNONLINEARSOLVER_H
#define NEWTONNONLINEARSOLVER_H

namespace Flash
{
// the Newton-Raphson method to solve nonlinear-equations
template<typename Function, typename FunctionPrime>
double NewtonRaphson(Function function, FunctionPrime derivative, double initialGuess, double tolerance = 1.0E-4, unsigned maxIterations = 100)
{
        // Auxiliary variables.
        double xNew = 0.0;
        double xOld = initialGuess;

        for(unsigned iter = 0; iter < maxIterations; ++iter)
        {
                xNew = xOld - function(xOld) / derivative(xOld);

                if(fabsf(xNew - xOld)/xNew < tolerance) break;

                xOld = xNew;
        }

        return xNew;
}

// the Newton-Raphson method to solve nonlinear-equations with built-in numerical derivatives
template<typename Function>
double NewtonRaphson(Function function, double initialGuess, double tolerance = 1.0E-4, unsigned maxIterations = 100)
{
        // Auxiliary variables.
        double xNew = 0.0;
        double xOld = initialGuess;
        const double epsilon = 1.0E-6;

        for(unsigned iter = 0; iter < maxIterations; ++iter)
        {
                xNew = xOld - 2.0 * epsilon * function(xOld) / (function(xOld + epsilon) - function(xOld - epsilon));

                if(fabsf(xNew - xOld)/xNew < tolerance) break;

                xOld = xNew;
        }

        return xNew;
}
} // namespace Flash

#endif /* NEWTONNONLINEARSOLVER_H */

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