Special Issue "Convolution Equations: Theory, Numerical Methods and Applications"
Deadline for manuscript submissions: 30 November 2023 | Viewed by 463
Interests: numerical analysis; approximation theory; singular and hypersingular integrals and integral equations; stability theory; dynamical systems; indentification methods; mathematical methods in geophysics and immunology
Convolution equations and related Riemann and Hilbert boundary value problems comprise an active and growing field in mathematics. This field involves a large number of independent but closely related disciplines. Convolution equations also include singular integral equations, hypersingular integral equations, Wiener–Hopf equations, integral equations with fractional integrals and derivatives, and many others.
It is not easy to list all areas in physics, engineering, and natural sciences where convolution equations play a key role, but some include: aerodynamics, electrodynamics, elasticity theory, automatic control theory, astrophysics, wave theory, materials science, and others.
Although many subjects known as “Convolution equations” have been known for over a century, they are being actively developed today.
Besides the branches mentioned above, singular integral equations and the related Riemann and Hilbert boundary value problems on fractals have been been actively studied over the last few decades.
In this Special Issue, we will present the current state of these areas and trace the connections between them.
This Special Issue will include works devoted to analytical methods for solving hypersingular integral equations, as well as approximate methods for solving weakly singular convolutional integral equations (Volterra and Fredholm), singular integral equations, hypersingular and polyhypersingular integral equations (linear and nonlinear) defined on various manifolds, integral equations with fractional integrals, Wiener–Hopf equations, Ambartsumian–Chandrasekhar equations, and systems of equations, which play an important role in the theory of light scattering in turbid media.
Numerical methods for solving integral equations rely upon efficient numerical methods for integral evaluation. This Special Issue also presents works dedicated to approximate methods for calculating singular and hypersingular integrals.
Prof. Dr. Ilya Boykov
Dr. Alla Boykova
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- weakly singular convolutional integral equations (Volterra and Fredholm)
- singular, hypersingular, and polyhypersingular integral equations
- approximate methods
- integral equations with fractional integrals
- Ambartsumian–Chandrasekhar systems of equations
- Wiener–Hopf equations