Contributions to the development of differential systems exactly solved by multistep finite-difference schemes. (English) Zbl 1201.65132
Summary: The motivation underlying this contribution is to complete some of the topics concerning exact schemes for numerically solving ordinary differential equations. A procedure for obtaining differential systems exactly solved by a given finite-difference method is described. Examples illustrating the application of the procedure for obtaining first-order, second-order and systems of differential equations exactly solved by different numerical methods are given. Among the numerical methods considered there are the trapezoidal rule, the two-step Adams-Bashforth method and the Numerov method. Some numerical examples are presented to provide evidence that the procedure works properly.
MSC:
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
Keywords:
exact finite-difference methods; nonstandard finite-difference methods; initial value problems; trapezoidal rule; two-step Adams-Bashforth method; Numerov method; numerical examplesSoftware:
MathematicaReferences:
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