Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations

Solving a nonlinear fractional differential equation using Chebyshev wavelets

Numerical solution of differential equations using Haar wavelets

A study of fractional Lotka-Volterra population model using Haar wavelet and Adams-Bashforth-Moulton methods

Numerical solution of evolution equations by the Haar wavelet method

An operational matrix of integration based on Haar wavelets is established, and a procedure for applying the matrix to analyse lumped and distributed-parameters dynamic systems is formulated. The technique can be interpreted from the incremental and multiresolution viewpoint. Crude as well as accurate solutions can be obtained by changing the parameter m; in the mean time, the main features of the solution are preserved. Several nontrivial examples are included for demonstrating the fast, flexible and convenient capabilities of the new method.

C.H. Hsiao

Papers

Haar wavelet method for solving lumped and distributed-parameter systems