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math.NA2021
Application of a Generalized Secant Method to Nonlinear Equations with Complex Roots
Avram Sidi
The secant method is a very effective numerical procedure used for solving nonlinear equations of the form . In a recent work [A. Sidi, Generalization of the secant method…
math.NA2021
PVTSI$^{\boldmath(m)}$: A Novel Approach to Computation of Hadamard Finite Parts of Nonperiodic Singular Integrals
Avram Sidi
We consider the numerical computation of $I[f]=\intBar^b_a f(x)\,dx$, the Hadamard Finite Part of the finite-range singular integral , with…
math.NA2021
Exactness and Convergence Properties of Some Recent Numerical Quadrature Formulas for Supersingular Integrals of Periodic Functions
Avram Sidi
In a recent work, we developed three new compact numerical quadrature formulas for finite-range periodic supersingular integrals $I[f]=\intBar^b_a f(x)\,dx$, where $f(x)=g(x)/(x-t)…
math.NA2021
Unified Compact Numerical Quadrature Formulas for Hadamard Finite Parts of Singular Integrals of Periodic Functions
Avram Sidi
We consider the numerical computation of finite-range singular integrals $$I[f]=\intBar^b_a f(x)\,dx,\quad f(x)=\frac{g(x)}{(x-t)^m},\quad m=1,2,\ldots,\quad a<t<b,$$ that are defi…