A New Collocation Method for Fuzzy Singular Integro-Differential Equations

In this article, a singular integro-differential equation has been considered under the notion of fuzziness. A new type of polynomial collocation method based on Jacobi polynomial has been studied to find the numerical solution of fuzzy singular integro differential equation in weighted space. In the polynomial collocation method, it is necessary to write the equation in terms of residual function. So, we have written the equation in terms of residual function and put the collocation points in the residual function to find the solution of the proposed equation. Also, the equation has been written in operator form. These operators help to prove the convergence of the proposed method. The convergence analysis of the polynomial collocation method has been given in terms of different types of lemmas and theorems. The algorithm of the proposed method has been given in the numerical example section, which briefly helps to understand the proposed method. A numerical example has been investigated to demonstrate the performance of the proposed method by providing different kinds of error analysis. Also, We have compared different types of error analysis in different weighted spaces. The error analysis has been investigated by providing different types of tables and figures. Finally, a comparison of our method with other existing methods have been presented which shows the effectiveness of our proposed method. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.