Shifted Chebyshev-Based Methods for Solution of Nonlinear Differential Equations
DOI:
https://doi.org/10.23918/eajse.v11i2p14Keywords:
Chebyshev Polynomials, Shifted Chebyshev Polynomial, Ordinary Differential Equation, Nonlinear Equations, Numerical AprroximationAbstract
In this study, we have used the Shifted Chebyshev technique to solve nonlinear ODEs. The method is to rewrite the problem in a more stable form using Shifted Chebyshev polynomials, which have proven efficient and accurate
in numerical solutions. The application of this method enables dealing with sophisticated nonlinear equations and makes it easy to find approximate solutions within a short time. The paper points out the advantages of the method in question, namely, diminished computational needs and better accuracy, and is exemplified by practical exercises. The current analysis concerning solving nonlinear ordinary differential equations using the Shifted Chebyshev technique offers a straightforward and readily applicable solution. Numerical results obtained from the proposed method show the precise agreement with the exact solution with minimum errors that outperforms the existing methods. Several examples are solved to show the effectiveness of the proposed method.
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