Related papers: Solving Volterra Integro-Differential Equations in…
In this paper, the iterative method developed by Daftardar-Gejji and Jafari (DJ method) is employed for analytic treatment of Laplace equation with Dirichlet and Neumann boundary conditions. The method is demonstrated by several physical…
Volterra's integral equations with local and nonlocal loads represent the novel class of integral equations that have attracted considerable attention in recent years. These equations are a generalisation of the classic Volterra integral…
We study error propagation in both an explicit and an implicit method for solving Volterra integro-differential equations. We determine the relationship between local and global errors. We derive upper bounds for the global error, and show…
The solution of integro-differential equations have a major role in the fields of science and engineering. Different approaches both numerical and analytic are used to solve these type of equations. In this paper, the solution of fuzzy…
A new method is given for proving the global existence of the solution to nonlinear Volterra integral equations. A bound on the solution is derived. The results are based on a nonlinear inequality proved by the author earlier.
We propose a spectral collocation method, based on the generalized Jacobi wavelets along with the Gauss-Jacobi quadrature formula, for solving a class of third-kind Volterra integral equations. To do this, the interval of integration is…
In this article, we explore two distinct issues. Initially, we examine the utilization of the Pontriagin maximum principle in relation to fractional delay differential equations. Additionally, we discuss the optimal approach for solving the…
We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give…
The paper considers the integral Volterra equations of the first kind which are related to the inverse boundary-value heat conduction problem. The algorithms have been developed to numerically solve the respective integral equations, which…
The numerical method for solution of the weakly regular scalar Volterra integral equation of the 1st kind is proposed. The kernels of such equations have jump discontinuities on the continuous curves which starts at the origin. The…
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…
Dynamic systems characterized by second-order nonlinear ordinary differential equations appear in many fields of physics and engineering. To solve these kinds of problems, time-consuming step-by-step numerical integration methods and…
In this paper, a two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel is proposed to reduce the computation time and improve the accuracy of the scheme…
In this paper, we present a collocation method for nonlinear Volterra integral equation of the first kind. This method benefits from the idea of $hp$-version projection methods. We provide an approximation based on the Legendre polynomial…
A Sinc-Nystr\"om method for Volterra integro-differential equations was developed by Zarebnia in 2010. The method is quite efficient in the sense that exponential convergence can be obtained even if the given problem has endpoint…
In this work, we present a collocation method based on the Legendre wavelet combined with the Gauss--Jacobi quadrature formula for solving a class of fractional delay-type integro-differential equations. The problem is considered with…
This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical…
This study investigates the existence and uniqueness of solutions to Volterra integral equations with discontinuous kernels in both linear and nonlinear cases. The problem is two-dimensional, and the collocation method is employed to…
In this paper, we investigate existence and uniqueness of solutions of nonlinear Volterra-Fredholm impulsive integrodifferential equations. Utilizing theory of Picard operators we examine data dependence of solutions on initial conditions…
The aim of this paper is to provide a comprehensive analysis of the path-dependent Stochastic Volterra Integral Equations (SVIEs), in which both the drift and the diffusion coefficients are allowed to depend on the whole trajectory of the…