Preservation of stability and oscillation of Euler-Maclaurin method for differential equation with piecewise constant arguments of alternately advanced and retarded type. (English) Zbl 1335.65064
Summary: This paper is devoted to stability and oscillation analysis of Euler-Maclaurin method for differential equation with piecewise constant arguments \(u'(t)=au(t)+bu(2[(t+1)/2])\). The necessary and sufficient conditions under which the numerical stability regions contain the analytical stability regions are given. Moreover, the conditions of oscillation for the Euler-Maclaurin method are obtained. We show that the Euler-Maclaurin method preserves the oscillation of the exact solution. In addition, the connection between stability and oscillation are discussed theoretically and numerically. Finally, some numerical examples are also provided.
MSC:
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65L07 | Numerical investigation of stability of solutions to ordinary differential equations |
| 34K28 | Numerical approximation of solutions of functional-differential equations (MSC2010) |
| 65L03 | Numerical methods for functional-differential equations |
| 34K11 | Oscillation theory of functional-differential equations |
Keywords:
Euler-Maclaurin method; stability; oscillation; piecewise constant arguments; numerical examplesReferences:
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