Mathematics and Statistics Vol. 10(1), pp. 74 - 87
DOI: 10.13189/ms.2022.100106
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Solving Ordinary Differential Equations (ODEs) Using Least Square Method Based on Wang Ball Curves

Abdul Hadi Bhatti ^*, Sharmila Binti Karim
Department of Mathematics & Statistics, School of Quantitative Sciences, Universiti Utara Malaysia, 06010 UUM Sintok, Kedah, Malaysia

ABSTRACT

Numerical methods are regularly established for the better approximate solutions of the ordinary differential equations (ODEs). The best approximate solution of ODEs can be obtained by error reduction between the approximate solution and exact solution. To improve the error accuracy, the representations of Wang Ball curves are proposed through the investigation of their control points by using the Least Square Method (LSM). The control points of Wang Ball curves are calculated by minimizing the residual function using LSM. The residual function is minimized by reducing the residual error where it is measured by the sum of the square of the residual function of the Wang Ball curve's control points. The approximate solution of ODEs is obtained by exploring and determining the control points of Wang Ball curves. Two numerical examples of initial value problem (IVP) and boundary value problem (BVP) are illustrated to demonstrate the proposed method in terms of error. The results of the numerical examples by using the proposed method show that the error accuracy is improved compared to the existing study of Bézier curves. Successfully, the convergence analysis is conducted with a two-point boundary value problem for the proposed method.

KEYWORDS
Wang Ball Curves, Ordinary Differential Equations, Least Square Methods, Residual Function

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Abdul Hadi Bhatti , Sharmila Binti Karim , "Solving Ordinary Differential Equations (ODEs) Using Least Square Method Based on Wang Ball Curves," Mathematics and Statistics, Vol. 10, No. 1, pp. 74 - 87, 2022. DOI: 10.13189/ms.2022.100106.

(b). APA Format:
Abdul Hadi Bhatti , Sharmila Binti Karim (2022). Solving Ordinary Differential Equations (ODEs) Using Least Square Method Based on Wang Ball Curves. Mathematics and Statistics, 10(1), 74 - 87. DOI: 10.13189/ms.2022.100106.