Improving Homotopy Analysis Method with An Optimal Parameter for Time-Fractional Burgers Equation
Aslı Alkan
2022Karamanoğlu Mehmetbey Üniversitesi Mühendislik ve Doğa Bilimleri Dergisi18 citationsDOIOpen Access PDF
Abstract
The aim of the study is to reduce the absolute error by determining the optimal value of this arbitrary parameter using the residual error function related to the selection of the arbitrary parameter h. Some numerical examples are solved and compared to existing results. The homotopy analysis method has been successfully implemented to Burgers equation to obtain serial solutions. On the base of the solutions obtained for the required equations, it has been shown that this method is applicable to time-fractional partial differential equations.
Topics & Concepts
MathematicsResidualApplied mathematicsPartial differential equationHomotopy analysis methodHomotopySelection (genetic algorithm)Differential equationFunction (biology)Mathematical analysisComputer scienceAlgorithmPure mathematicsBiologyArtificial intelligenceEvolutionary biologyFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNumerical methods in engineering