Numerical solution of time-varying systems with a stretch by general Legendre wavelets

Using the general Legendre wavelets a function with a stretch is expanded. The property of the general operational matrix of integration is given and the general Legendre wavelets stretch matrix is introduced. The direct algorithm for a product of a matrix function and a vector function is proposed. Furthermore the time-varying systems with a stretch are solved by the general Legendre wavelets. The numerical examples illustrate that the algorithms are applicable.