NUMERICAL SOLUTION DIFFERENTIAL EQUATION VIA CUBIC HERMITE LEAST SQUARE METHOD

The present manuscript aims to give the details of the application of the finite elements method which is based upon the cubic Hermite Least Squares (CHLSM) method to a widely used prototype test problem. The fundamental objective of the present study is to establish a foundation for applying the Least Squares finite element method which is based upon cubic Hermite basis functions to different types of differential equations, including fractional, partial, and ordinary order equations. The explanation of the method on the differential equation under consideration, its application, and the simulation of the program written with the obtained scheme are detailed in the present study. The main contribution of the present study is to show the application of Cubic Hermite Least Squares Method on a typical model problem. The handled problem is selected as an ordinary differential equation for easy presentation of the method, but researchers can easily apply the presented method for other ordinary, partial even fractional order differential equations.