In this research paper, an improved Chebyshev-Gauss-Lobatto pseudospectral approximation of nonlinear Burger-Huxley and Fitzhugh- Nagumo equations have been presented. The method employs chebyshev Gauss-Labatto points in time and space to obtain spectral accuracy. The mapping has introduced and transformed the initial-boundary value non-homogeneous problem to homogeneous problem. The main probl...

We present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is compatible low order finite volume (FV) type discretizations that allow for convex blending with the variant goal guaranteeing additional properties, such as bounds on physical quantities and/or guaranteed entropy dissipation. For an ...

The success of the classical formulation of the spectral element method lies in the choice of functional space, grid points, and method of integration. On the quadrilateral, the prefered space is a tensor product basis of Legendre polynomials, P 2 = fspan(x n y m)j0 m N; 0 n Ng: (1) The grid points are chosen as the Gauss-Lobatto-Legendre points, which lead to an accurate, well-behaved interpol...

‎A numerical technique based on the collocation method using Legendre multiwavelets are‎ ‎presented for the solution of forced Duffing equation‎. ‎The operational matrix of integration for ‎Legendre multiwavelets is presented and is utilized to reduce the solution of Duffing equation‎ ‎to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate‎ ‎the valid...

In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on whi...

In the context of numerical methods for conservation laws, not only the preservation of the primary conserved quantities can be of interest, but also the balance of secondary ones such kinetic energy in case of the Euler equations of gas dynamics. In this work, we construct a kinetic energy preserving discontinuous Galerkin method on Gauss-Legendre nodes based on the framework of summation-by-p...

— We construct and analyze efficient fully discrete Galerkin type methods, that are of high order of accuracy and conservative in the L sense,for approximating the solution ofaform of the linear Schrödinger équation with a time-dependent coefficient, found e.g. in underwater acoustics. The time stepping procedures are based on the class of implicit Runge-Kutta methods known as the q-stage Gauss...