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Homotopy Analysis Method and Physics-Informed Neural Networks for Solving Volterra Integral Equations with Discontinuous Kernels

Axioms
This paper addresses first- and second-kind Volterra integral equations (VIEs) with discontinuous kernels. A hybrid method combining the Homotopy Analysis Method (HAM) and Physics-Informed Neural Networks (PINNs) is developed.
Samad Noeiaghdam, Md Asadujjaman Miah, Sanda Micula   +2 more
doaj   +2 more sources

Kernel estimation of discontinuous regression functions

Statistics and Probability Letters, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ja-Yong Koo, Kee-Hoon Kang
exaly   +2 more sources

An Algorithm for Solving Phase-Lag Nonlinear Mixed Integral Equation With Discontinuous Generalized Kernel

Advances in Mathematical Physics
In this work, a nonlinear fractional integrodifferential equation (NFIo-DE) with discontinuous generalized kernel in position and time is explored in space L2Ω×C0,T ...
Abeer M. Al-Bugami, M. A. Abdou
doaj   +2 more sources

Application of the Godunov-Type Corrective Smoothed Particle Method to Impulsive Load Studies [PDF]

Journal of Applied Fluid Mechanics, 2022
The smoothed particle hydrodynamics (SPH) method is based on the kernel particle approximation, which is sensitive to the uniformity of the SPH particle distribution in the computational domain; that is, all SPH particles must be distributed evenly in ...
M. Zhang, J. M. Zhang
doaj   +1 more source

The Numerical Validation of the Adomian Decomposition Method for Solving Volterra Integral Equation with Discontinuous Kernels Using the CESTAC Method

Mathematics, 2021
The aim of this paper is to present a new method and the tool to validate the numerical results of the Volterra integral equation with discontinuous kernels in linear and non-linear forms obtained from the Adomian decomposition method.
Samad Noeiaghdam, Denis Sidorov, Abdul-Majid Wazwaz, Nikolai Sidorov, Valery Sizikov   +4 more
doaj   +1 more source

Polynomial Spline Collocation Method for Solving Weakly Regular Volterra Integral Equations of the First Kind

Известия Иркутского государственного университета: Серия "Математика", 2022
The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels.
Aleksandr Tynda, Samad Noeiaghdam, Denis Sidorov   +2 more
doaj   +1 more source

A Physical Phenomenon for the Fractional Nonlinear Mixed Integro-Differential Equation Using a Quadrature Nystrom Method

Fractal and Fractional, 2023
In this work, the existence and uniqueness solution of the fractional nonlinear mixed integro-differential equation (FrNMIoDE) is guaranteed with a general discontinuous kernel based on position and time-space  L2Ω×C0,T ...
A. R. Jan, M. A. Abdou, M. Basseem
doaj   +1 more source

Physical phenomena of spectral relationships via quadratic third kind mixed integral equation with discontinuous kernel

AIMS Mathematics, 2023
Spectral relationships explain many physical phenomena, especially in quantum physics and astrophysics. Therefore, in this paper, we first attempt to derive spectral relationships in position and time for an integral operator with a singular kernel ...
S. Alhazmi, M. A. Abdou, M. Basseem
semanticscholar   +1 more source

On a class of integral equations with discontinuous kernels [PDF]

Transactions of the American Mathematical Society, 1927
This paper is given to the discussion of the integral equation in which the kernel K(x, t) is continuous, but possesses first partial derivatives which are discontinuous along the line t = x. It is closely related to a previous papert in which the case of a discontinuous kernel has been treated.
Rudolph E. Langer, Eleanor P. Brown
openaire   +1 more source

The C_2 heat-kernel coefficient in the presence of boundary discontinuities [PDF]

Classical and Quantum Gravity, 1997
25 pages ...
Apps, J. S., Dowker, J. S.
openaire   +4 more sources