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Variable order Adams codes. (English) Zbl 1035.65076

Summary: Variable step size, variable order (VSVO) Adams codes are very effective for solving initial value problems for first-order systems of ordinary differential equations. The theory of fixed-order codes is classical, but when the order is varied, there is no theory explaining fundamental issues. With realistic assumptions about order and step size selection, we prove convergence, approximate locally the behavior of the error, and justify standard error estimators.

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
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