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...

an analytical solution of the equation describing diffusion of intrinsic point defects in semiconductor crystals has been obtained for a one-dimensional finite-length domain with the robin-type boundary conditions. the distributions of point defects for different migration lengths of defects have been calculated. the exact analytical solution was used to verify the approximate numerical solutio...

We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...

the paper presents the semi-numerical solution for the magnetohydrodynamic (mhd) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. the governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (node) by using a classical similarity transformation along with appropriate boundary cond...

‎A computational technique for solution of mathematical model of gas solution in a fluid is presented‎. ‎This model describes the change of mass of the gas volume due to diffusion through the contact surface‎. ‎An appropriate representation of the solution based on the M"{u}ntz polynomials reduces its numerical treatment to the solution of a linear system of algebraic equations‎. ‎Numerical exa...