Second Chebyshev wavelet operational matrix of integration and its application in the calculus of variations

Abstract

In this paper, we extend the application of the second Chebyshev wavelet (SCW) method to solve variational problems and establish a clear solving procedure for this kind of problems. An operational matrix of integration based on the SCW is presented and a general procedure for forming this matrix is given. The main characteristic of SCW operational matrix method is that it can transform a variational problem to a system of algebraic equations. Thus, it can simplify the variational problems solving. The proposed method is illustrated by some applications, which can show the validity of the present approach.

Keywords:

• second Chebyshev wavelets
• direct method
• variational problem
• operational matrix of integral
• product operation matrix

2000 AMS Subject Classifications:

• 65L05
• 65L10
• 65T60