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Partial differential equations with highly oscillatory input terms are hardlyever solvable analytically and their numerical treatment is difficult.Modulated Fourier expansion used as an {\it ansatz} is a well known andextensively investigated tool in asymptotic numerical approach for this kind ofproblems. Although the efficiency of this approach has been recognised, itserror analysis has not been investigated rigorously for general forms of linearPDEs. In this paper, we start such kind of investigations for a general form oflinear PDEs with an input term characterised by a single high frequency. Moreprecisely we derive an analytical form of such an expansion and provide aformula for the error of its truncation. Theoretical investigations areillustrated by computational simulations.

Asymptotic expansions for the linear PDEs with oscillatory input terms; Analytical form and error analysis