Chebyshev Differential Quadrature for Numerical Solutions of Higher Order Singular Perturbation Problems
For researchers in numerical analysis and applied mathematics, this work offers a numerical approach for solving higher order singular perturbation problems, but it is incremental as it applies an existing method (differential quadrature) with Chebyshev polynomials to a specific class of problems.
This study applies the Chebyshev differential quadrature method to solve linear and nonlinear higher order singularly perturbed problems, demonstrating accuracy and effectiveness through comparison with exact solutions.
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient matrix which is necessary to get numerical results. Following this, different class of perturbation problems are considered as test problems. Then, all results are shown in tables and also comparison between numerical and exact solution shows the accuracy and effectiveness of the presented method.