# Evolution scheme to compute periodic solutions of first-order nonlinear equations containing translation operators

• J. J. Keller
• W. Egli
Original Papers

## Summary

An evolution scheme is proposed to compute periodic solutions of equations of the general form
$$f\frac{{df}}{{dt}} + Lf = 0,$$
whereL is a linear operator which may include translations. The convergence properties of the proposed scheme are investigated and compared with the convergence properties of alternative numerical solution methods. The application of the evolution scheme is illustrated with the computation of solutions of equations arising in nonlinear wave propagation.

### Keywords

Wave Propagation Linear Operator Periodic Solution Mathematical Method Nonlinear Equation

## Zusammenfassung

Zur Berechnung periodischer Lösungen von Gleichungen der Form
$$f\frac{{df}}{{dt}} + Lf = 0,$$
wird ein Evolutionsschema vorgeschlagen. Hierbei seiL ein linearer Operator, der beispielsweise auch Translationsoperatoren enthalten darf. Die Konvergenzeigenschaften des Schemas werden untersucht und mit den Konvergenzeigenschaften anderer numerischer Lösungsmethoden verglichen. Die Anwendung des Evolutionsschemas wird an Beispielen nichtlinearer Wellengleichungen erläutert.

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