A note on solving integro-differential equation with Cauchy kernel

Hermite Polynomial and Least-Squares Technique for Solving Integro-differential Equations

“…Using airfoil polynomials of the first kind, examines the numerical solution for a class of IDE with Cauchy kernel. Obtain a system of linear algebraic equations using this strategy [2]. With weakly singular kernels, a new collocation type approach for solving VIE of the second sort has been developed.…”

The Iterated Projection Method for Integro-Differential Equations With Cauchy Kernel

“…In [10], the authors have discussed the superconvergence of the Galerkin iterates for integral equations of the second kind. In [6], we have studied projection approximations for solving Cauchy integro-differential equations using airfoil polynomials of the first kind. In [7], we have applied the successive approximation method, for solving a Cauchy singular integral equations of the first kind in the general case.…”

Wavelet method applied to specific adhesion of elastic solids via molecular bonds

“…18 For coupled nonlinear singular integro-differential equations, the power series based iterative algorithm has been adopted by Wang and Gao 12 and Wang et al 13 Applications of this method involves the calculation of a number of Cauchy type singular integrals, which usually needs sophisticated mathematical skills. In order to avoid this cumbersome situation and establish a generally efficient mathematical tool to solve a broad range of strong nonlinear mathematical problems arising from molecular and cellular biomechanics studies, we adopt a recently developed wavelet based numerical method for the solution of the adhesion problems in the present study.…”