TY - CHAP
T1 - Numerical Solutions of Delay Differential Equations
AU - Rihan, Fathalla A.
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
PY - 2021
Y1 - 2021
N2 - In many application areas, one finds evolutionary problems with an after-effect whose numerical solution is based on the use of an integrator for ODEs combined with a suitable continuous extension. Our aim in this chapter is to survey numerical methods for solving DDEs and NDDEs based on modified ODE formulae. Special emphasis is given to continuous Runge-Kutta methods that have been used by the author. We describe, in brief, the theory of accuracy and some issues related to numerical solutions of DDEs and NDDEs.
AB - In many application areas, one finds evolutionary problems with an after-effect whose numerical solution is based on the use of an integrator for ODEs combined with a suitable continuous extension. Our aim in this chapter is to survey numerical methods for solving DDEs and NDDEs based on modified ODE formulae. Special emphasis is given to continuous Runge-Kutta methods that have been used by the author. We describe, in brief, the theory of accuracy and some issues related to numerical solutions of DDEs and NDDEs.
UR - http://www.scopus.com/inward/record.url?scp=85113821665&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85113821665&partnerID=8YFLogxK
U2 - 10.1007/978-981-16-0626-7_2
DO - 10.1007/978-981-16-0626-7_2
M3 - Chapter
AN - SCOPUS:85113821665
T3 - Forum for Interdisciplinary Mathematics
SP - 23
EP - 49
BT - Forum for Interdisciplinary Mathematics
PB - Springer
ER -