in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...

the coast of bangladesh has a specialty in terms of high bending and many off- shore islands. incorporation of the coastline and island boundaries properly in the numerical scheme is essential for accurate estimation of water levels due to surge. for that purpose a numerical scheme consisting of very fine mesh is required along the coastal belt, whereas this is unnecessary away from the coast. in...

in this paper, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of tvd (total variation diminishing) of the solution, is proposed. this scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. schemes preserving the essential physical property of tvd are of great importance in practice. such s...

in recent years, the number of research works devoted to applying the highly accurate numerical schemes, in particular compact finite difference schemes, to numerical simulation of complex flow fields with multi-scale structures, is increasing. the use of compact finite-difference schemes are the simple and powerful ways to reach the objectives of high accuracy and low computational cost. compa...

we develope a numerical method based on b-spline collocation method to solve linear klein-gordon equation. the proposed scheme is unconditionally stable. the results of numerical experiments have been compared with the exact solution to show the efficiency of the method computationally. easy and economical implementation is the strength of this approach.

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...

In this paper, a numerical scheme is proposed for the multi-fluid compressible flows. This method is applied to the problem of underwater explosion. The proposed scheme is basically the extension of Godunov method in gas dynamic problems to the multifluid environments and is second-order accurate in space. In this method, also, the problem of artificial mixing of two different phases on Euleria...

In this paper, a numerical scheme is proposed for the multi-fluid compressible flows. This method is applied to the problem of underwater explosion. The proposed scheme is basically the extension of Godunov method in gas dynamic problems to the multifluid environments and is second-order accurate in space. In this method, also, the problem of artificial mixing of two different phases on Euleria...