dev.nm.analysis.differentialequation.ode.ivp.solver.extrapolation

Class SemiImplicitExtrapolation

java.lang.Object

dev.nm.analysis.differentialequation.ode.ivp.solver.extrapolation.SemiImplicitExtrapolation

All Implemented Interfaces:

ODESolver

public class SemiImplicitExtrapolation
extends Object
implements ODESolver

Semi-Implicit Extrapolation is a method of solving ordinary differential equations, that is similar to Burlisch-Stoer extrapolation. However, instead of using the regular explicit Euler's method to compute mid-point estimates, this algorithm uses a Taylor series approximation to the implicit backward Euler's method: \[ x_{k+1} = x_k + h f(t_{k+1}, x_{k+1}) \]

This method is more computationally expensive but has a tendency to remain stable for larger step sizes. In particular, it is useful for solving stiff ODEs.

See Also:

Wikipedia: Explicit and implicit methods

Constructor Summary

Constructors

Constructor and Description
SemiImplicitExtrapolation(double epsilon, int maxIterations) Create an instance of this algorithm with the given precision parameter and the maximum number of iterations allowed.

Method Summary

Modifier and Type	Method and Description
ODESolution	solve(ODE1stOrder ode) Solves the given ODE problem.
ODESolution	solve(ODE1stOrderWith2ndDerivative ode)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SemiImplicitExtrapolation

public SemiImplicitExtrapolation(double epsilon,
                                 int maxIterations)

Create an instance of this algorithm with the given precision parameter and the maximum number of iterations allowed.

Parameters:

epsilon - the relative precision required

maxIterations - the maximum number of iterations

Method Detail

solve

public ODESolution solve(ODE1stOrder ode)

Description copied from interface: ODESolver

Solves the given ODE problem.

Specified by:

solve in interface ODESolver

Parameters:

ode - the ODE problem

Returns:

the solution

solve

public ODESolution solve(ODE1stOrderWith2ndDerivative ode)