A Fundamental Solution for a Biharmonic Finite-Difference Operator

A Fundamental Solution for a Biharmonic Finite-Difference Operator1

A Fundamental Solution of N. Zeilon's Operator

A finite difference method for the smooth solution of linear Volterra integral equations

The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...

A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method

In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...

On the existence of solution for a $k$-dimensional system of three points nabla fractional finite difference equations

In this paper, we investigate the existence of solution for a k-dimensional system of three points nabla fractional finite difference equations. Also, we present an example to illustrate our result.