In this paper, we present a mixed spline/spectral method to solve Volterra delay-integro-differential equations (VDIDEs). This method is based on generating the sextic spline collocation methods in all subintervals. The approximation of the integration in these subintervals, can be calculated by the El-Gendi method. Convergence results of the present method are presented. Numerical results are ...

Differential quadrature method DQM is proposed for the numerical solution of oneand twospace dimensional hyperbolic telegraph equation subject to appropriate initial and boundary conditions. Both polynomial-based differential quadrature PDQ and Fourier-based differential quadrature FDQ are used in space directions while PDQ is made use of in time direction. Numerical solution is obtained by usi...

We present a general framework for a higher-order spline level-set (HLS) method and apply this to bio-molecule surfaces construction. Starting from a first order energy functional, we obtain a general level set formulation of geometric partial differential equation, and provide an efficient approach to solve this partial differential equation using a C(2) spline basis. We also present a fast cu...

. In this paper, we develop a quadratic spline collocation method for integrating the nonlinear partial differential equations (PDEs) of a plug flow reactor model. The method is proposed in order to be used for the operation of control design and/or numerical simulations. We first present the Crank-Nicolson method to temporally discretize the state variable. Then, we develop and analyze the pro...

in this paper, the effect of different boundary conditions on the free vibration analysis response of a sandwich plates is presented using higher order shear deformation theory. the face sheets are orthotropic laminated composite that follow the first order shear deformation theory (fsdt) based on rissners-mindlin (rm) kinematics field. based on energy method and hamilton's principle, the ...

In this paper, a numerical algorithm using a coupled Galerkin-Differential Quadrature (DQ) method is proposed for the solution of dam-reservoir interaction problem. The governing differential equation of motion of the dam structure is discretized by the Galerkin method and the DQM is used to discretize the fluid domain. The resulting systems of ordinary differential equations are then solved by...

Isogeometric analysis (IGA) has been recently introduced as a viable alternative to the standard, polynomial-based finite element analysis. One of the fundamental performance issues of the isogeometric analysis is the quadrature of individual components of the discretized governing differential equation. The capability of the isogeometric analysis to easily adopt basis functions of high degree ...

Many mathematical formulations of physical phenomena contain integro-differential equations. In this paper a numerical method is developed to solve the convection-diffusion integro-differential equations with a weakly singular kernel using the cubic B-spline collocation method. These equations occur in many applications such as in the transport of air and ground water pollutants, oil reservoir ...

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula.The error analysis of proposed numerical method is studied theoretically. Numerical results are given toil...