Subdomain collocation method based on successive integration technique for solving delay differential equations

C. Kayelvizhi and A. Emimal Kanaga Pushpam *

Department of Mathematics, Bishop Heber College (Autonomous), Tiruchirappalli – 620 017, Affiliated to Bharathidasan University, Tamilnadu, India.
 
Research Article
International Journal of Science and Research Archive, 2024, 11(02), 382–390.
Article DOI: 10.30574/ijsra.2024.11.2.0429
Publication history: 
Received on 31 January 2024; revised on 08 March 2024; accepted on 11 March 2024
 
Abstract: 
The main objective of this work is to propose the polynomial based Subdomain collocation method using successive integration technique for solving delay differential equations (DDEs). In this study, the most widely used classical orthogonal polynomials, namely, the Bernoulli polynomial, the Chebyshev polynomial, the Hermite polynomial, and the Fibonacci polynomial are considered. Numerical examples of linear and nonlinear DDEs have been considered to demonstrate the efficiency and accuracy of the method. Approximate solutions obtained by the proposed method are well comparable with exact solutions. From the results it is observed that the accuracy of the numerical solutions by the proposed method increases as N (order of the polynomial) increases. The proposed method is very effective, simple, and suitable for solving the linear and nonlinear DDEs in real-world problems.
 
Keywords: 
Orthogonal polynomials; Subdomain collocation method; Successive integration technique; Delay differential equations; Pantograph
 
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