In this paper, using the hyperbolic uniform spline of order 4 we develop the classes of methods for the numerical solution of second order boundary value problems (2VBP) with Dirichlet, Neumann and Cauchy types boundary conditions. The second derivativeis approximated by the three-point central difference scheme. The approximate results, obtained by the proposed method, confirm theconvergence o...

Keywords: Differential quadrature method Hyperbolic telegraph equation Modified B-spline basis functions Thomas algorithm a b s t r a c t The present paper uses a relatively new approach and methodology to solve second order two dimensional hyperbolic telegraph equation numerically. We use modified cubic B-spline basis functions based differential quadrature method for space discretization that...

Abstract Via modified quartic hyperbolic B-spline DQM, Burgers’ equation is numerically approximated in the current study. Ten numerical instances are discussed, and findings compared with those already existence exact results. Error norms assessed, shown tabular as well graphical formats, to validate resilience applicability portion of established system. Matrix stability analysis approach use...

In this paper, a collocation finite difference scheme based on new cubic trigonometric B-spline is developed and analyzed for the numerical solution of a one-dimensional hyperbolic equation (wave equation) with non-local conservation condition. The usual finite difference scheme is used to discretize the time derivative while a cubic trigonometric B-spline is utilized as an interpolation functi...

Elliptic and hyperbolic partial differential equation methods for generating both surface and volume structured grids have been implemented in the Gridgen software system. Their implementation provides the means by which very high quality quad and hex grids can be generated for computational fluid dynamics (CFD). The grids, in turn, provide the basis for highly accurate CFD simulations of visco...

By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...