Mikhlin’s Integral Equation and the Integral Equation with the Generalized Neumann Kernel on Simply Connected Domains

Numerical Conformal Mapping via a Boundary Integral Equation with the Adjoint Generalized Neumann Kernel

This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral equation is derived by reformulating the conformal mapping as an adjoint Riemann-Hilbert problem. From the adjoint Riemann-Hilbert problem, we derive a bound...

Fredholm-Volterra integral equation and generalized potential kernel

A method is used to solve the Fredholm–Volterra integral equation of the first kind in the space L2ðXÞ Cð0; T Þ, X 1⁄4 ðx; yÞ 2 X: ffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 þ y2 p n 6 a; z 1⁄4 0 o and T < 1: The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class Cð1⁄2X 1⁄2X Þ, while the kernel of the Volterra integral term is a positive an...

On the Volterra Integral Equation with Weakly Singular Kernel

Fredholm-volterra Integral Equation with Potential Kernel

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω)×C(0,T ),Ω = {(x,y) : √ x2+y2 ≤ a}, z = 0, and T <∞. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω]×[Ω]), while the kernel of Volterra integral term is a positive and continuous function that belongs to the class C[0,T ]. Also in...

A Boundary Integral Equation with the Generalized Neumann Kernel for a Certain Class of Mixed Boundary Value Problem

1 Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia 2 Department of Mathematics, Faculty of Science, Ibb University, P.O. Box 70270, Ibb, Yemen 3 Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia 4 Ibnu Sina Institute for Fundamental Science Studies, Universiti Tek...