Arnold, M.; Simeon, B. Pantograph and catenary dynamics: A benchmark problem and its numerical solution. (English) Zbl 0964.65101 Appl. Numer. Math. 34, No. 4, 345-362 (2000). Summary: Coupled systems of partial differential equations and differential-algebraic equations (DAEs) are of actual interest in various practical applications. From this point of view we have recently studied the intersection of pantograph and catenary in high speed trains. To stimulate further research on this topic we formulate in the present paper a simplified model problem that reflects basic parts of the nonlinear dynamics in the technical system pantograph/catenary. Following the method of lines the equations of motion are semi-discretized in space using finite differences. For time discretization, typical DAE techniques are applied such as index reduction, projection steps and handling of systems with varying structure. Cited in 1 ReviewCited in 16 Documents MSC: 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 34A09 Implicit ordinary differential equations, differential-algebraic equations 65L80 Numerical methods for differential-algebraic equations 35L35 Initial-boundary value problems for higher-order hyperbolic equations 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs Keywords:semidiscretization; pantograph equation; catenary equation; coupled problems; benchmark problem; partial differential-algebraic equations; systems; method of lines; finite differences; index reduction PDFBibTeX XMLCite \textit{M. Arnold} and \textit{B. Simeon}, Appl. Numer. Math. 34, No. 4, 345--362 (2000; Zbl 0964.65101) Full Text: DOI