Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 254-265 |
| Number of pages | 12 |
| Journal | Journal of Computational Mathematics |
| Volume | 27 |
| Issue number | 2 |
| Publication status | Published - Apr 2009 |
Scopus Subject Areas
- Computational Mathematics
User-Defined Keywords
- Spectral methods
- Legendre quadrature formula
- Pantograph-type delay differential equations
- Error analysis
- Exponential convergence