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...

We prove that every rational angled hyperbolic triangle has transcendental side lengths and that every rational angled hyperbolic quadrilateral has at least one transcendental side length. Thus, there does not exist a rational angled hyperbolic triangle or quadrilateral with algebraic side lengths. We conjecture that there does not exist a rational angled hyperbolic polygon with algebraic side ...

In this work, a computational method for solving nonlinear Volterra-Fredholm-Hammerestein integral equations is proposed. Compactly supported semiorthogonal cubic B-spline wavelets are employed as basis functions then collocation method is utilized to reduce the computation of integral equations to some algebraic system. The method is computationally attractive, and applications are demonstrate...

In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville in...

Abstract—In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of propose...

In this paper (part three of the trilogy) we use low degree G 1 and G 2 continuous regular algebraic spline curves deened within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize curve families whose members have the required interpolating properties and possess a minimal number of innection points. The regular algebraic spline curves consider...