Recursive higher order fuzzy transform method for numerical solution of Volterra integral equation with singular and nonsingular kernels

Abstract In the present paper, the continuous form of the higher degree Fuzzy transform (F m -transform) technique is used for the numerical solution of the second kind Volterra integral equations with singular and nonsingular kernels. By employing this method, the equation is converted to the system of linear algebraic equations with a lower Hessenberg coefficient matrix. It is shown that the coefficient matrix is invertible. The error analysis is carried out for the solution procedure. The results show that for singular kernels, the accuracy decreases with an increasing degree of fuzzy transform due to the non-differentiability of the kernel. Experiments on nonsingular kernels show convergence with an increasing degree of fuzzy transform. As expected, the accuracy of the method improves with partition numbers for both singular and nonsingular kernels. Some examples are given to illustrate the theoretical results.