Approximate Solution of Higher Order Fuzzy Initial Value Problems of Ordinary Differential Equations Using Bezier Curve Representation

The Bezier curve is a parametric curve used in the graphics of a computer and related areas. This curve, connected to the polynomials of Bernstein, is named after the design curves of Renault's cars by Pierre Bézier in the 1960s. There has recently been considerable focus on finding reliable and more effective approximate methods for solving different mathematical problems with differential equations. Fuzzy differential equations (known as FDEs) make extensive use of various scientific analysis and engineering applications. They appear because of the incomplete information from their mathematical models and their parameters under uncertainty. This article discusses the use of Bezier curves for solving elevated order fuzzy initial value problems (FIVPs) in the form of ordinary differential equation. A Bezier curve approach is analyzed and updated with concepts and properties of the fuzzy set theory for solving fuzzy linear problems. The control points on Bezier curve are obtained by minimizing the residual function based on the least square method. Numerical examples involving the second and third order linear FIVPs are presented and compared with the exact solution to show the capability of the method in the form of tables and two dimensional shapes. Such findings show that the proposed method is exceptionally viable and is straightforward to apply.