We propose a novel numerical approach for delay differential equations with vanishing proportional delays based on spectral methods. A Legendre-collocation method is employed to obtain highly accurate numerical approximations to the exact solution. It is proved theoretically and demonstrated numerically that the proposed method converges exponentially provided that the data in the given pantograph delay differential equation are smooth.
|Number of pages||12|
|Journal||Journal of Computational Mathematics|
|Publication status||Published - Mar 2009|
Scopus Subject Areas
- Computational Mathematics
- Spectral methods; Legendre quadrature formula; Pantograph-type delay differential equations; Error analysis; Exponential convergence