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Rapid variable-step computation of dynamic convolutions and Volterra-type integro-differential equations: RK45 Fehlberg, RK4. [PDF]

Heliyon
Ndi Azese M.
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Adequacy of Standard Models for Long-Term Behavior of Lightweight Concrete with Sintered Aggregate Under Cyclic Loading. [PDF]

Materials (Basel)
Lewiński PM, Fedorczyk Z, Więch P, Zacharski Ł.   +3 more
europepmc   +1 more source

Comparison of the Performance of Nonlinear Time-Dependent Constitutive Models Calibrated with Minimal Test Data Applied to an Epoxy Resin. [PDF]

Materials (Basel)
Guedes RM, Morais JL.
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On a Nonlinear Volterra Integral-Functional Equation

On a Nonlinear Volterra Integral-Functional Equation
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Volterra integral equations and nonlinear semigroups

Nonlinear Analysis: Theory, Methods & Applications, 1977
Publisher Summary This chapter discusses Volterra integral equations and nonlinear semigroups. It presents the nonlinear Volterra integral equation x ( t ) = y ( t ) + ∫ g ( t − s , x ( s )) ds , t ≥ 0, where H is a Hilbert space, y : [0, ∞) → H is given, g : [0, ∞) × H → satisfies a Lipschitz condition in its second place, and x :
G F Webb
exaly   +2 more sources

On some parameter methods for nonlinear Volterra integral equation

Applied Mathematics and Computation, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Nonlinear Volterra Integral Equations and the Apéry Identities

Bulletin of the London Mathematical Society, 1992
The authors study necessary and sufficient conditions for the existence of nontrivial solutions of the Volterra integral equation \(u(x)=\int_ 0^ x k(x-s) g(u(s))ds\). Using the identity \[ \begin{multlined} \int_ a^ x f(s)h(s)ds= \int_ a^ \lambda f(s)\varphi(s)ds+ \int_ a^ \lambda [f(\lambda-f(s)][\varphi(s)-h(s)]ds+\\ +\int_ \lambda^ x [f(s)- f ...
Bushell, P. J., Okrasiński, W.
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On nonlinear Fredholm–Volterra integral equations with hysteresis

Applied Mathematics and Computation, 2004
The author improves his earlier result concerning the existence and uniqueness of solutions of the following Fredholm-Volterra system with hysteresis \[ x(t)= g(t)+ \int^t_0 p(t,s)\phi(s, x(s), w[S[x]](s))\,ds+ \int^\infty_0 q(t,s) \psi(s, x(s), w[S[x]](s))\,ds,\tag{1} \] where \(w\) denotes a hysteresis operator and \(S\) is the superposition operator
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NONLINEAR VOLTERRA INTEGRAL EQUATIONS WITH CONVOLUTION KERNELS

Bulletin of the London Mathematical Society, 2003
Some new results concerning the existence and uniqueness of nontrivial solutions to the title equations are presented.
Mydlarczyk, W., Okrasiński, W.
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Nonlinear volterra integral equations of the first kind

Nonlinear Analysis: Theory, Methods & Applications, 1995
Consider the weakly singular Volterra systems of the first kind \[ \int_0^t {k \bigl( t,s,x(s) \bigr) \over (t - s)^\alpha} ds = f(t), \qquad t \in J = [0,a], \tag{*} \] where \(\alpha \in [0,1)\), \(k : \Delta \times \mathbb{R}^n \to \mathbb{R}^n\) with \(\Delta = \{(s,t) \in J^2 : s \leq t\}\) and \(f : J \to \mathbb{R}^n\) are given.
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