On the Pseudo-Spectral Method of Solving Linear Ordinary Differential Equations
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Date
2009
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Abstract
Not all differential equations can be solved analytically, to overcome this problem, there is need to search for an accurate approximate solution. Approach: The objective of this study was to find an accurate approximation technique (scheme) for solving linear differential equations. By exploiting the Trigonometric identity property of the Chebyshev polynomial, we developed a numerical scheme referred to as the pseudo-pseudo-spectral method. Results: With the scheme developed, we were able to obtain approximate solution for certain linear differential equations. Conclusion: The numerical scheme developed in this study competes favorably with solutions obtained with standard and well known spectral methods. We presented numerical examples to validate our results and claim.
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Chebyshev polynomial, Linear ordinary differential equations, Spectral method, Pseudo-spectral method, Pseudo-pseudo-spectral method
Citation
Ogundare, B. S. (2009). On the Pseudo-Spectral Method of Solving Linear Ordinary Differential Equations. Journal of Mathematics and Statistics, 5(2): 136 - 140.