Finite element solution of a linear mixed-type functional differential equation

• Published in: Numerical algorithms Vol. 55; no. 2-3; pp. 301 - 320
• Main Authors: Lima, Pedro Miguel, Teodoro, M. Filomena, Ford, Neville J., Lumb, Patricia M.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.11.2010; Springer Nature B.V
• Subjects: Algebra; Algorithms; Approximation; Computer Science; Constants; Differential equations; Finite element method; Intervals; Mathematical analysis; Mathematical models; Numeric Computing; Numerical Analysis; Original Paper; Theory of Computation; Forward-backward differential equation; Collocation; Splines; 65Q05; Least squares; 34K06; 34K28; Method of steps; 34K10; Finite element
• ISSN: 1017-1398; 1572-9265
• DOI: 10.1007/s11075-010-9412-y

This paper is devoted to the approximate solution of a linear first-order functional differential equation which involves delayed and advanced arguments. We seek a solution x , defined for t  ∈ (0, k  − 1],( k  ∈  IN ), which takes given values on the intervals [ − 1, 0] and ( k  − 1, k ]. Continuing the work started in previous articles on this subject, we introduce and analyse a computational algorithm based on the finite element method for the solution of this problem which is applicable both in the case of constant and variable coefficients. Numerical results are presented and compared with the results obtained by other methods.