Study of Interval Type-2 Fuzzy Singular Integro-Differential Equation by Using Collocation Method in Weighted Space

Suvankar Biswas, Sandip Moi and Smita Pal
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Suvankar Biswas: Department of Mathematics, Sonarpur Mahavidyalaya, Kolkata 700149, India
Sandip Moi: ��Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B. Garden, Howrah 711103, India
Smita Pal: ��Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B. Garden, Howrah 711103, India

New Mathematics and Natural Computation (NMNC), 2022, vol. 18, issue 01, 113-145

Abstract: This paper develops the numerical solution of interval type-2 fuzzy singular integro-differential equation. The theory of polynomial collocation method has been introduced to find the numerical solution of interval type-2 fuzzy singular integro-differential equation in different weighted spaces. The equation has been presented in operator form. It has been shown that the operators are bounded which are required for the convergence of the proposed method. Theorems and lemmas have been developed to show the convergence of our proposed method in type-2 fuzzy environment. A numerical algorithm for the collocation method has been presented in the numerical section. A numerical example has been examined to show the validation of our proposed method. Different types of error analysis have been examined in the form of different types of tables and figures. Also, the comparison of different types of error analysis has been examined in different weighted space.

Keywords: Fuzzy differential equation; interval type-2 fuzzy differential equation; type-2 fuzzy integro-differential equation; polynomial collocation method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S1793005722500077

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