On the sparse multi-scale solution of the delay differential equations by an efficient algorithm

An efficient algorithm based on wavelet Galerkin method is proposed for solving the time-varying delay systems. According to the useful properties of Alpert's multiwavelets such as interpolation, orthonormality, flexible vanishing moments and sparsity, a time-varying system is reduced to the sparse linear system of algebraic equations. The results illustrate the error will not be greater than a certain amount while the number of nonzero coefficients is reduced by selecting the appropriate threshold. Therefore the computational cost is reduced using thresholding. The analysis of convergence has been investigated and the accuracy and efficiency of the proposed method are illustrated by several examples. © 2020 Elsevier Inc.