The numerical solution of neutral functional differential equations by Adams predictor-corrector methods. (English) Zbl 0748.65057
The authors consider the initial value problem for a functional differential equation of neutral type \(y'(t)=f(t,y(.),y'(.))\) \(t\in[a,b]\), \(y(t)=g(t)\) for \(t\in[\tau,a]\), where \(\tau\leq a<b\), \(f\) is a Volterra operator and \(g\) is a prescribed initial function. An algorithm for this problem based on an unequal interval Adams-Bashforth, Adams-Moulton predictor corrector method with stepsize control and order changing strategy based on the estimation of local discretization error by Milne’s device is described. Numerical results for miscellaneous problems are presented.
Reviewer: Z.Schneider (Bratislava)
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |
| 34K40 | Neutral functional-differential equations |
Keywords:
numerical examples; initial value problem; neutral type; algorithm; Adams-Bashforth, Adams-Moulton predictor corrector method; stepsize control; order changing strategyReferences:
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