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Nonlinear differential-algebraic equations (DAE) are typically solved using implicit stiff solvers based on backward difference formula or RADAU formula, requiring a Newton Raphson approach for the nonlinear equations or using Rosenbrock methods specifically designed for DAEs.
Specifically, the Gear's implicit integration method based on backward difference formula (BDF) is most suitable for this problem.
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It is well known from numerical analysis of differential equations that there are just discretisations based on backward (nabla) differences which enable to retain the key properties of underlying differential equations.
Implicit and semi-implicit time integration techniques based on backward differentiation and extrapolation formulae are considered.
On the one hand we extend these classes, on the other hand we introduce decidable classes based on backward chaining.
We use a methodology based on backward induction to calculate a pure Nash equilibrium for each game.
Bayesian group sequential design relies upon Bayesian decision-theoretic approaches based on backward induction, which is often computationally intensive.
Both methods yielded the same result and therefore only results based on backward elimination are presented.
For this procedure we retained variables based on backward elimination, p < 0.1.
Further selection of variables was based on backward elimination procedure using a LR-test at 0.05 as cut-point.
Stepwise regression analyses based on backward elimination were performed to test the influence of various factors on the vaspin serum concentrations.
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