Solution of variational problems via Haar orthonormal wavelet direct method

Abstract

This article establishes a clear procedure for the variational problem solution via the Haar orthonormal wavelet technique. The variational problems are solved by means of the direct method using the Haar orthonormal wavelets and reduced to the solution of algebraic equations. The local property of the Haar orthonormal wavelets is fully applied to shorten the calculation process in the task. Three illustrative examples and a practical application to a heat conduction problem are included.

Keywords:

• Haar orthonormal wavelet
• Variational problem
• Direct method