Department of Mathematics
Collocation methods for differential equations with piecewise linear delays
After analyzing the regularity of solutions to delay differential equations (DDEs) with piecewise continuous (linear) non-vanishing delays, we describe collocation schemes using continuous piecewise polynomials for their numerical solution. We show that for carefully designed meshes these collocation solutions exhibit optimal orders of global and local superconvergence analogous to the ones for DDEs with constant delays. Numerical experiments illustrate the theoretical superconvergence results.
Collocation methods, Delay differential equations, Optimal order of superconvergence, Piecewise non-vanishing delays, Regularity of solutions
Source Publication Title
Communications on pure and applied analysis
American Institute of Mathematic
Liang, Hui, and Hermann Brunner. "Collocation methods for differential equations with piecewise linear delays." Communications on pure and applied analysis 11.5 (2012): 1839-1857.