Class SemiImplicitExtrapolation
- java.lang.Object
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- dev.nm.analysis.differentialequation.ode.ivp.solver.extrapolation.SemiImplicitExtrapolation
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- 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
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Constructor Summary
Constructors Constructor Description SemiImplicitExtrapolation(double epsilon, int maxIterations)
Create an instance of this algorithm with the given precision parameter and the maximum number of iterations allowed.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description ODESolution
solve(ODE1stOrder ode)
Solves the given ODE problem.ODESolution
solve(ODE1stOrderWith2ndDerivative ode)
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Constructor Detail
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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 requiredmaxIterations
- the maximum number of iterations
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Method Detail
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solve
public ODESolution solve(ODE1stOrder ode)
Description copied from interface:ODESolver
Solves the given ODE problem.
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solve
public ODESolution solve(ODE1stOrderWith2ndDerivative ode)
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