An Efficient Numerical Algorithm For Solving Linear Differential Equations of Arbitrary Order an‎d Coefficients

Referring to one of the recent works of the authors, presented in [13], for numerical solution of linear dierential equations, an alternative scheme is proposed in this article to considerably improve the accuracy and eciency. For this purpose, triangular functions as a set of orthogonal functions are used. By using a special representation of the vector forms of triangular functions and the related operational matrix of integration, solving the dierential equation reduces to solve a linear system of algebraic equations. The formulation of the method is quite general, such that any arbitrary linear dierential equation may be solved by it. Moreover, the algorithm does not include any integration and, instead, uses just sampling of functions, that results in a lower computational complexity. Also, the formulation of this approach needs no modication when a singularity occurs in the coecients of dierential equation. Some problems are numerically solved by the proposed method to illustrate that it is much more accurate and applicable than the prior method in [13].