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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Suvankar Biswas & Sandip Moi & Smita Pal, 2022. "Study of Interval Type-2 Fuzzy Singular Integro-Differential Equation by Using Collocation Method in Weighted Space," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 113-145, March.
    • Handle: RePEc:wsi:nmncxx:v:18:y:2022:i:01:n:s1793005722500077
    DOI: 10.1142/S1793005722500077
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