In this work we compare semi-discrete formulations to obtain numerical solutions for the 1D Burgers equation. The formulations consist in the discretization of the time-domain via multi-stage methods of second and fourth order: R11 and R22 Padé approximants, and of the spatial-domain via finite element methods: least-squares (MEFMQ), Galerkin (MEFG) and Streamline-Upwind Petrov-Galerkin (SUPG)....

An orthogonal subspace minimization method is developed for finding multiple (eigen) solutions to the defocusing nonlinear Schrödinger equation with symmetry. Since such solutions are unstable, gradient search algorithms are very sensitive to numerical errors, will easily break symmetry, and will lead to unwanted solutions. Instead of enforcing a symmetry by the Haar projection, the authors use...

In this paper we present a numerical scheme for solving Burgers equation using B-spline finite element method. Main advantages of the present technique are: it is simple, efficient and moreover easy to understand. Some numerical examples are considered to test the functioning of proposed scheme. Results obtained from the given method of solution are validated by means of comparisons made with t...

Numerical solutions of the full Navier-Stokes equations are obtained for the problem of natural convection in closed cavities of small aspect ratio with differentially heated end walls. These solutions cover the parameter range Pr = 6.983, 10 6 Gr d 2 x lo4 and 0.05 4 A d 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solution...

In this paper, reproducing kernel method is proposed for solving singularly perturbed fourth order boundary value problem in 5 2 W [0,1] . The exact solutions are given in the form of series. By truncating the series, the app-roximate solutions is obtained. The errors of the approximate solutions are monotone decreasing with the increasing of nodal points. It is observed that our approach produ...

We study a system of partial differential equations derived from the FitzHugh-Nagumo model. In one dimension solutions are required to satisfy zero Dirichlet boundary conditions on the interval Ω = (−1, 1). Estimates are given to describe bounds on the range of parameters over which solutions exist; numerical computations provide the global bifurcation diagram for families of symmetric and asym...

In this paper, two analytic solutions for the valuation of European-style Parisian and Par. asian options under the Black-Scholes framework are, respectively, presented. A key feature of our solution procedure is the reduction of a three-dimensional problem to a two-dimensional problem through a coordinate transform designed to combine the two time derivatives into one. Compared with some previ...

in this paper we apply hybrid functions of general block-pulse‎ ‎functions and legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (fdes)‎. ‎our approach is based on incorporating operational matrices of‎ ‎fdes with hybrid functions that reduces the fdes problems to‎ ‎the solution of algebraic systems‎. ‎error estimate that verifies a‎ ‎converge...

in this paper operational matrix of bernstein polynomials (bps) is used to solve bratu equation. this nonlinear equation appears in the particular elecotrospun nanofibers fabrication process framework. elecotrospun organic nanofibers have been used for a large variety of filtration applications such as in non-woven and filtration industries. by using operational matrix of fractional integration...

In this work we generate the numerical solutions of the Burgers’ equation by applying the Crank-Nicolson method directly to the Burgers’ equation, i.e., we do not use Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. Absolute error of the present method is compared to the absolute error of the two existing methods for two test problems. The method is also analy...