A New Convergent Pseudospectral Method for Delay Differential Equations

• Published in: Iranian journal of science and technology. Transaction A, Science Vol. 44; no. 1; pp. 203 - 211
• Main Authors: Mahmoudi, M., Ghovatmand, M., Noori Skandari, M. H.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-02-2020
• Subjects: Chemistry/Food Science; Earth Sciences; Engineering; Life Sciences; Materials Science; Mathematics; Physics; Research Paper; Delay differential equations; Shifted Legendre pseudospectral method; Nonlinear programming
• ISSN: 1028-6276; 2364-1819
• DOI: 10.1007/s40995-019-00812-3

Delay differential equations have a wide range of applications in science and engineering. When these equations are nonlinear, we cannot usually obtain an exact solution. Hence, we must utilize an efficient numerical method with high convergence rate and low error to approximate the solution. In this paper, we propose a new shifted pseudospectral method to solve nonlinear delay differential equations. First, we convert the problem into an equivalent continuous-time optimization problem and then use a pseudospectral method to discretize the problem. By solving the obtained discrete-time problem, we achieve an approximate solution for the main delay differential equation. Here, we analyze the convergence of the method and solve some practical delay differential equations to show the efficiency of the method.