On the Pseudo-Spectral Method of Solving Linear Ordinary Differential Equations

Abstract

<b>Problem statement:</b> Not all differential equations can be solved analytically, to overcome this problem, there is need to search for an accurate approximate solution. <b>Approach</b>: 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. <b>Results</b>: With the scheme developed, we were able to obtain approximate solution for certain linear differential equations. <b>Conclusion:</b> 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