A Novel Projection Method for Cauchy-Type Systems of Singular Integro-Differential Equations

Abstract

This article introduces a new projection method via shifted Legendre polynomials and an efficient procedure for solving a system of integro-differential equations of the Cauchy type. The proposed computational process solves two systems of linear equations. We demonstrate the existence of the solution to the approximate problem and conduct an error analysis. Numerical tests provide theoretical results.

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

“…The area of energy dissipation, or the hole area, was reduced to a limited uniform domain using the present methodology; we achieved this by using a certain conformal mapping z = cζ(τ), where c > 0 to provide the solution to the boundary value problem as a discontinuous kernel integrodifferential equation. This kind of integrodifferential equation plays a famous role in many important applications of contact problems in elastic media and material engineering sciences; see [33][34][35]. The Cauchy technique is a powerful tool that allows us to simplify the singular or super-strong singular problem, enabling us to handle it more efficiently.…”

Solving System of Mixed Variational Inclusions Involving Generalized Cayley Operator and Generalized Yosida Approximation Operator with Error Terms in q-Uniformly Smooth Space

“…The Cayley transform is a mapping between skew symmetric matrices and special orthogonal matrices. In real, complex, and quaternionic analysis, many applications of the Cayley transform can be found (see [31][32][33][34]).…”