A new operational matrix of derivative for Chebyshev wavelets and its applications in solving ordinary differential equations with non analytic solution (Q2906035)

The authors propose to use a Galerkin method based on Chebyshev wavelets for the solution of initial or boundary value problems in ordinary differential equations. To realize this approach, the differentiation matrix representing higher derivatives is derived. The claim that this yields an efficient integrator for problems with non-analytic solutions is illustrated by several numerical examples, where the coefficients and solutions may display singularities, but not substantiated by comparisons with established standard discretization methods.