Haar wavelet collocation method for linear first order stiff differential equations

¹ Mechanical Engineering, Abdullah Gul University
² Mechatronics Engineering, Sabanci University

^* e-mail: mehmettarik.atay@agu.edu.tr
^** e-mail: onurmetin.mertaslan@agu.edu.tr
^*** e-mail: musakasim.agca@agu.edu.tr
^**** e-mail: abdulkadir.yilmaz@agu.edu.tr
^† e-mail: toker@sabanciuniv.edu

Abstract

In general, there are countless types of problems encountered from different disciplines that can be represented by differential equations. These problems can be solved analytically in simpler cases; however, computational procedures are required for more complicated cases. Right at this point, the wavelet-based methods have been using to compute these kinds of equations in a more effective way. The Haar Wavelet is one of the appropriate methods that belongs to the wavelet family using to solve stiff ordinary differential equations (ODEs). In this study, The Haar Wavelet method is applied to stiff differential problems in order to demonstrate the accuracy and efficacy of this method by comparing the exact solutions. In comparison, similar to the exact solutions, the Haar wavelet method gives adequate results to stiff differential problems.