Class JSci.maths.NumericalMath
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Class JSci.maths.NumericalMath
java.lang.Object
|
+----JSci.maths.NumericalMath
- public final class NumericalMath
- extends Object
The numerical math library.
This class cannot be subclassed or instantiated because all methods are static.
-
differentiate(int, Mapping, double, double)
- Numerical differentiation.
-
euler(double[], Mapping, double)
- Uses the Euler method to solve an ODE.
-
gaussian4(int, Mapping, double, double)
- Numerical integration using the Gaussian integration formula (4 points).
-
gaussian8(int, Mapping, double, double)
- Numerical integration using the Gaussian integration formula (8 points).
-
leapFrog(double[], Mapping, double)
- Uses the Leap-Frog method to solve an ODE.
-
metropolis(double[], Mapping, double)
- The Metropolis algorithm.
-
richardson(int, Mapping, double, double)
- Numerical integration using the Richardson extrapolation.
-
rungeKutta(double[], Mapping, double)
- Uses the Runge-Kutta method to solve an ODE.
-
simpson(int, Mapping, double, double)
- Numerical integration using Simpson's rule.
-
trapezium(int, Mapping, double, double)
- Numerical integration using the trapezium rule.
euler
public static double[] euler(double y[],
Mapping func,
double dt)
- Uses the Euler method to solve an ODE.
- Parameters:
- y - an array to be filled with y values, set y[0] to initial condition
- func - -dy/dt
- dt - step size
- Returns:
- y
leapFrog
public static double[] leapFrog(double y[],
Mapping func,
double dt)
- Uses the Leap-Frog method to solve an ODE.
- Parameters:
- y - an array to be filled with y values, set y[0],y[1] to initial conditions
- func - -dy/dt
- dt - step size
- Returns:
- y
rungeKutta
public static double[] rungeKutta(double y[],
Mapping func,
double dt)
- Uses the Runge-Kutta method to solve an ODE.
- Parameters:
- y - an array to be filled with y values, set y[0] to initial condition
- func - -dy/dt
- dt - step size
- Returns:
- y
trapezium
public static double trapezium(int N,
Mapping func,
double a,
double b)
- Numerical integration using the trapezium rule.
- Parameters:
- N - the number of strips to use
- func - a function
- a - the first ordinate
- b - the last ordinate
simpson
public static double simpson(int N,
Mapping func,
double a,
double b)
- Numerical integration using Simpson's rule.
- Parameters:
- N - the number of strip pairs to use
- func - a function
- a - the first ordinate
- b - the last ordinate
richardson
public static double richardson(int N,
Mapping func,
double a,
double b)
- Numerical integration using the Richardson extrapolation.
- Parameters:
- N - the number of strip pairs to use (lower value)
- func - a function
- a - the first ordinate
- b - the last ordinate
gaussian4
public static double gaussian4(int N,
Mapping func,
double a,
double b)
- Numerical integration using the Gaussian integration formula (4 points).
- Parameters:
- N - the number of strips to use
- func - a function
- a - the first ordinate
- b - the last ordinate
gaussian8
public static double gaussian8(int N,
Mapping func,
double a,
double b)
- Numerical integration using the Gaussian integration formula (8 points).
- Parameters:
- N - the number of strips to use
- func - a function
- a - the first ordinate
- b - the last ordinate
differentiate
public static double[] differentiate(int N,
Mapping func,
double a,
double b)
- Numerical differentiation.
- Parameters:
- N - the number of points to use
- func - a function
- a - the first ordinate
- b - the last ordinate
metropolis
public static double[] metropolis(double list[],
Mapping func,
double dx)
- The Metropolis algorithm.
- Parameters:
- list - an array to be filled with values distributed according to func, set list[0] to initial value
- func - distribution function
- dx - step size
- Returns:
- list
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