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.
Highlights
Diverse types of engineering and practical problems are explained and interpreted as stiff ordinary differential equations (ODEs) [1]
Knowing only the differential equation is not sufficient to find the solutions to the problem, meaning that the need for extra information is evident
When all the components of y are defined in terms of x, which is specified at a certain value, the problem can be classified as "Initial Value Problem"
Summary
Diverse types of engineering and practical problems are explained and interpreted as stiff ordinary differential equations (ODEs) [1]. While some problems can be solved by analytical methods, some cases are not always suitable for having an analytical solution This factor itself is not the only reason to use numerical approaches. Since the proposed solution to the given stiff linear ODE is an initial value problem (IVP), the explanation of extra information can be said as "Initial Conditions". The Haar Wavelet Method is used to solve such differential equations numerically. The aim of this work is to discuss the quality, efficiency and accuracy of the Haar wavelet method for solving linear stiff ODEs with initial conditions. When the required computation power and low error deviation is taken into consideration, the proposed solution shows the effectiveness of Haar Wavelet Method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
