Asymptotic Methods of ODEs: Exploring Singularities of the Second Kind
arXiv:1110.22631.21 citationsh-index: 6
Originality Incremental advance
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Provides a novel method for stabilizing numerical solutions of ODEs with singularities, benefiting computational mathematics.
The paper develops symbolic asymptotic methods for linear ODEs to stabilize numerical calculations by recasting equations in mollified form, achieving stability.
We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use to them stabilize numerical calculations. Our method follows classical analysis for first-order systems and higher-order scalar equations where growth behavior is expressed in terms of elementary functions. We then recast our equations in mollified form - thereby obtaining stability.