One-Leg Formulas for Stiff Ordinary Differential Equations
Copyright policy )One-Leg Formulas for Stiff Ordinary Differential Equations
Some one-leg formulae for stiff ordinary differential equations, that are a generalization of the backward differentiation formulae, are obtained. Applied to the standard scalar test problem, \(y'=\lambda y\), with step length h, these new formulae give large regions of instability in the right half-plane \(Re(h\lambda)>0\). This property makes the formulae more suitable than the backward differentiation formulae for the detection of unstable problems. Numerical results are given.
regions of instability, region of absolute stability, test problem, Linear ordinary differential equations and systems, one-leg formulae, backward differentiation formulae, Numerical results, Numerical methods for initial value problems involving ordinary differential equations, Stability and convergence of numerical methods for ordinary differential equations, stiff equations
regions of instability, region of absolute stability, test problem, Linear ordinary differential equations and systems, one-leg formulae, backward differentiation formulae, Numerical results, Numerical methods for initial value problems involving ordinary differential equations, Stability and convergence of numerical methods for ordinary differential equations, stiff equations
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