Variable order Adams codes. (English) Zbl 1035.65076

Shampine, L. F.

Comput. Math. Appl. 44, No. 5-6, 749-761 (2002).

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

Keywords:

Adams codes; Variable order; Convergence; Error estimation; variable step size; initial value problems; first-order systems

Software:

Matlab; ode113; ode23s; MATLAB ODE suite; ode45; Ode15s; ode23

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