Solving neutral delay differential equations using least square method based on successive integration technique

C. Kayelvizhi and A. Emimal Kanaga Pushpam *

Department of Mathematics, Bishop Heber College (Autonomous), Tiruchirappalli – 620 017, Affiliated to Bharathidasan University, Tamilnadu, India.
 
Review
International Journal of Science and Research Archive, 2024, 11(02), 509–517.
Article DOI: 10.30574/ijsra.2024.11.2.0474
Publication history: 
Received on 09 February 2024; revised on 16 March 2024; accepted on 19 March 2024
 
Abstract: 
The main objective of this work is to propose the Least square method (LSM) using successive integration technique for solving Neutral delay differential equations (NDDEs). Continuous LSM and Discrete LSM have been presented by adopting different orthogonal polynomials as weighted basis functions. 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 NDDEs have been provided 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 NDDEs in real-world problems.
 
Keywords: 
Least square method; Neutral delay differential equations; Orthogonal polynomials; Successive integration technique
 
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