Incorporating Fuzziness in the Traditional Runge–Kutta Cash–Karp Method and Its Applications to Solve Autonomous and Non-Autonomous Fuzzy Differential Equations

Nurain Zulaikha Husin, Muhammad Zaini Ahmad () and Mohd Kamalrulzaman Md Akhir
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Nurain Zulaikha Husin: Institute of Engineering Mathematics, Universiti Malaysia Perlis, Arau 02600, Perlis, Malaysia
Muhammad Zaini Ahmad: Institute of Engineering Mathematics, Universiti Malaysia Perlis, Arau 02600, Perlis, Malaysia
Mohd Kamalrulzaman Md Akhir: Institute of Engineering Mathematics, Universiti Malaysia Perlis, Arau 02600, Perlis, Malaysia

Mathematics, 2022, vol. 10, issue 24, 1-25

Abstract: The study of the fuzzy differential equation is a topic that researchers are interested in these days. By modelling, this fuzzy differential equation can be used to resolve issues in the real world. However, finding an analytical solution to this fuzzy differential equation is challenging. Thus, this study aims to present the fuzziness in the traditional Runge–Kutta Cash–Karp of the fourth-order method to solve the first-order fuzzy differential equation. Later, this method is referred to as the fuzzy Runge–Kutta Cash–Karp of the fourth-order method. There are two types of fuzzy differential equations to be solved: autonomous and non-autonomous fuzzy differential equations. This fuzzy differential equation is divided into the (i) and (ii)–differentiability on the basis of the characterization theorem. The convergence analysis of the fuzzy Runge–Kutta Cash–Karp of the fourth-order method is also presented. By implementing the fuzzy Runge–Kutta Cash–Karp of the fourth-order method, the approximate solution is compared with the analytical and numerical solutions obtained from the fuzzy Runge–Kutta of the fourth-order method. The results demonstrated that the approximate solutions of the proposed method are accurate with an analytical solution, when compared with the solutions of the fuzzy Runge–Kutta of the fourth-order method.

Keywords: fuzzy number; Runge–Kutta Cash–Karp; fuzzy differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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