Convergence Analysis of Discretization Methods for Nonlinear First Kind Volterra Integral Equations.
Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type
In this paper, we deal with a system of integral algebraic equations of the Hessenberg type. Using a new index definition, the existence and uniqueness of a solution to this system are studied. The well-known piecewise continuous collocation methods are used to solve this system numerically, and the convergence properties of the perturbed piecewise continuous collocation methods are investigated to obtain the order of convergence for the given numerical methods. Finally, some numerical experiments...
Convergence domains under Zabrejko-Zinčenko conditions using recurrent functions
We provide a semilocal convergence analysis for Newton-type methods using our idea of recurrent functions in a Banach space setting. We use Zabrejko-Zinčenko conditions. In particular, we show that the convergence domains given before can be extended under the same computational cost. Numerical examples are also provided to show that we can solve equations in cases not covered before.
Convex solutions of a nonlinear integral equation of Urysohn type.
Corrections to the article `Weighted Monte Carlo methods for approximate solution of a nonlinear Boltzmann equation'.
Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation
In this paper the control system with limited control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The admissible control functions are chosen from the closed ball centered at the origin with radius in
Discounted optimal stopping for maxima in diffusion models with finite horizon.
Efficient algorithms for solving nonlinear Volterra integro-differential equations with two point boundary conditions.
Ein Beitrag zur Verzweigungstheorie.
Ein nichtlineares Schwingungsproblem mit gemischter linearer Randbedingung.
Elliptic perturbations for Hammerstein equations with singular nonlinear term.
Equations with discontinuous nonlinear semimonotone operators
The aim of this paper is to present an existence theorem for the operator equation of Hammerstein type with the discontinuous semimonotone operator . Then the result is used to prove the existence of solution of the equations of Urysohn type. Some examples in the theory of nonlinear equations in are given for illustration.
Equivalence of Volterra integral equations
Error estimate in the sinc collocation method for Volterra-Fredholm integral equations based on DE transformation.
Error evaluation of approximate solutions for sum-difference equations in two variables.
Evolution in a changing environment: existence of solutions
We establish the existence of solutions of an intrinsically nonlinear differential-integral equation that arises from the mathematical modelling of the evolution of an asexual population in a changing environment. The main objective is to pave the way for a rigorous analysis of the linear stability of travelling wave solutions of the corresponding problem.
Existence and analytic approximation of solutions of Duffing type nonlinear integro-differential equation with integral boundary conditions.
Existence and approximate solutions of nonlinear integral equations.
Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation
Mathematics Subject Classification: 45G10, 45M99, 47H09We study the solvability of a perturbed quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions which are defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions. Finally, we give an example to illustrate our abstract results.
Existence and uniqueness of a solution to a partial integro-differential equation by the method of lines.