Mathematics· 2026Q2
Adaptive Adams-Type Methods Based on Algebraic, Trigonometric, and Exponential Interpolation
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- Q2SCImago
- 2026year
Short summary
A novel adaptive Adams-type method (ATE) selects between algebraic, trigonometric, or exponential interpolation schemes at each step to solve ordinary differential equations, improving adaptability to solution behavior.
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Key points
- Introduces an adaptive Adams-type method (ATE) for ODEs.
- ATE selects between algebraic, trigonometric, or exponential interpolation schemes dynamically.
- Stability properties of trigonometric and exponential variants differ from the algebraic method.
- Numerical experiments validate accuracy and execution times across various ODEs.
AI-generated from the title and abstract; the full text is not read.
Abstract
We consider an adaptive Adams-type multistep method for the numerical solution of ordinary differential equations based on algebraic, trigonometric, and exponential interpolation (the ATE method). For each interpolation class, the corresponding schemes are derived following the same construction as classical Adams methods. The stability properties of the trigonometric and exponential variants are analyzed, highlighting their differences relative to the algebraic method. The adaptive ATE algorithm selects one of the three schemes at each step according to a local interpolation indicator. This enables the method to adjust to different types of solution behavior. Numerical experiments are presented across a variety of differential equations, and the accuracy and execution times of the methods are compared.
The authors' abstract, as published at the source. Mathematics, 2026 · DOI ↗
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Field: Numerical Analysis
Numerical AnalysisMathematics