Results 61 to 70 of about 2,553,181 (201)

Approximate Numerical Solutions for Linear Volterra Integral Equations Using Touchard Polynomials

مجلة بغداد للعلوم, 2020
In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation.
Jalil Talab Abdullah
doaj   +1 more source

Finite‐Block Polynomial and Volterra Structure in Reservoir Computing

Numerical Linear Algebra with Applications, Volume 33, Issue 4, August 2026.
ABSTRACT Reservoir computing is analyzed through the algebraic structure generated by finite‐width reservoirs on fixed input blocks. For linear and quadratic logistic activations, the induced input‐to‐state map admits an exact finite Volterra representation, yielding an explicit characterization of the associated hypothesis class.
Alfio Borzì
wiley   +1 more source

On solving a singular Volterra integral equation

Filomat
In the paper, a general solution of the singular Volterra integral equation of the second kind is found. The feature of the considered integral equation lies in the fact that the integral of its kernel does not tend to zero as the upper limit approaches the lower one, thus making the Picard method inapplicable.
Murat Ramazanov, Nurtay Kudaybergenovich Gulmanov, Madi Tulegenovich Omarov   +2 more
openaire   +1 more source

Uncertainty Quantification of Analytical Solutions for the Nonlinear Space and Time Fractional Order ϕ4$$ {\phi}^4 $$ Equation Under Fuzziness

Engineering Reports, Volume 8, Issue 7, July 2026.
Analytical fuzzy soliton solutions of a modified space–time fractional ϕ4$$ {\phi}^4 $$ model are derived using EHFM, capturing memory effects and uncertainty. Results reveal diverse wave structures and show how fractional order and fuzziness significantly influence soliton amplitude, localization, and propagation, with heightened sensitivity near the ...
Mohsin Khalid, Neha Andaleeb Khalid, Baboucarr Ceesay, Zafar Iqbal   +3 more
wiley   +1 more source

Coexistence, crossover and extirpation in coalescent communities and ecotones

Oikos, Volume 2026, Issue 7, July 2026.
When two ecological communities come into contact, the strength of their mixing determines whether species coexist, extirpate, or extend their ranges. We present analytical formulas and simulations describing these transitions. Specifically, we derive abundance shifts upon community coalescence, identify the critical mixing strength leading to first ...
Martin Heidelman, Dervis Can Vural
wiley   +1 more source

Numerical Treating of Mixed Integral Equation Two-Dimensional in Surface Cracks in Finite Layers of Materials

Advances in Mathematical Physics, 2022
The goal of this paper is study the mixed integral equation with singular kernel in two-dimensional adding to the time in the Volterra integral term numerically.
A. M. Al-Bugami
doaj   +1 more source

Solutions for singular Volterra integral equations

Electronic Journal of Qualitative Theory of Differential Equations, 2009
Summary: We consider the system of Volterra integral equations \[ \begin{multlined} u_i(t) =\int_{0}^{t}g_i(t,s)[P_i(s,u_1(s),u_2(s),\dots,u_n(s))+ \\ + Q_i(s,u_1(s),u_2(s),\dots,u_n(s))]ds,\quad t\in [0,T],\;1\leq i\leq n \end{multlined} \] where \(T>0\) is fixed and the nonlinearities \(P_i(t,u_1,u_2,\dots,u_n)\) can be singular at \(t=0\) and \(u_j ...
openaire   +4 more sources

Matsumura‐Type Estimates and Global Solutions of a Fractional Wave Equation With Nonlocal Nonlinearity

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9967-9983, June 2026.
ABSTRACT The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of εutt+ut+(−Δ)βu=0,u(0,x)=φ(x),ut(0,x)=ψ(x),$$ \varepsilon {u}_{tt}+{u}_t+{\left(-\Delta \right)}^{\beta }u=0,\kern1em u ...
Ibrahim Ahmad Suleman, Mokhtar Kirane
wiley   +1 more source

The Modified Camassa–Holm Equation on the Half Line: A Riemann–Hilbert Approach

Studies in Applied Mathematics, Volume 156, Issue 6, June 2026.
ABSTRACT We consider the initial‐boundary value (IBV) problem for the modified Camassa–Holm (mCH) equation m∼t+(u∼2−u∼x2+2u∼)m∼x=0,m∼:=u∼−u∼xx+1$\tilde{m}_t+{\left((\tilde{u}^2-\tilde{u}_x^2+2\tilde{u})\tilde{m}\right)}_x = 0, \qquad \tilde{m}:=\tilde{u}-\tilde{u}_{xx}+1$ on the half‐line x≥0$x \ge 0$.
Iryna Karpenko, Dmitry Shepelsky
wiley   +1 more source

Asymptotic solutions of linear Volterra integral equations with singular kernels [PDF]

Transactions of the American Mathematical Society, 1974
Volterra integral equations of the form u ′ ( t
Wong, J. S. W., Wong, R.
openaire   +2 more sources