Related papers: Solving fuzzy convolution Volterra integro-differe…
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…
In this work we prove that a family of explicit numerical finite-difference methods is convergent when applied to a nonlinear Volterra equation with a power-type nonlinearity. In that case the kernel is not of Lipschitz type, therefore the…
We address a linear fractional differential equation and develop effective solution methods using algorithms for inversion of triangular Toeplitz matrices and the recently proposed QTT format. The inverses of such matrices can be computed…
The article is devoted to the solvability of a system of integro-differential equations in the case of the difference of the standard Laplacian and the bi-Laplacian in the diffusion terms. The proof of the existence of solutions is based on…
We present a method derived from Laplace transform theory that enables the evaluation of fractional integrals. This method is adapted and extended in a variety of ways to demonstrate its utility in deriving alternative representations for…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
Convection-diffusion of heat transfer is one of the important phenomena in fluid flow and industrial problems. The involved parameters, boundary conditions, and material properties are greatly affecting the same. As such, the uncertainness…
We discuss the application of multistep collocation methods to Volterra integral equations which contain a weakly singular kernel $(t-\tau)^{\alpha-1}$ with $0 <\alpha <1.$ Convergence orders of the methods are determined and their…
A generalized summation by parts algorithm is presented for solving of difference equations of the form $T^m(y)-a[u]y=b[u]$ where $T$ denotes the shift $u_j\to u_{j+1}$. Solvability of such type of equations with respect to coefficients of…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
In the present paper, a Nystrom-type method for second kind Volterra integral equations is introduced and studied. The method makes use of generalized Bernstein polynomials, defined for continuous functions and based on equally spaced…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
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…
We establish pointwise formulas for the shape derivative of solutions to the Dirichlet problem associated with the fractional Laplacian. Specifically, we consider the equation $(-\Delta)^s u = h$ in $\Omega$ and $u=0$ in $\Omega^c$, where…
In this paper we describe a method to solve the linear non-homogeneous fractional differential equations (FDE), composed with Jumarie type Fractional Derivative, and describe this method developed by us, to find out Particular Integrals,…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…
We present a nonlinear partial difference equation defined on a square which is obtained by combining the Miura transformations between the Volterra and the modified Volterra differential-difference equations. This equation is not symmetric…
Random coupled parabolic partial differential models are solved numerically using random cosine Fourier transform together with non Gaussian random numerical integration that capture the highly oscillatory behavior of the involved…
We present implicit and explicit versions of a numerical algorithm for solving a Volterra integro-differential equation. These algorithms are an extension of our previous work, and cater for a kernel of general form. We use an appropriate…
The present study proposed a method for numerical solution of linear Volterra integral equations (VIEs) of the third kind, before only analytical solution methods had been discussed with reference to previous research and review of the…