Nabendra Parumasur

Pseudospectral Laguerre approximation of transport-fragmentation equations

We develop a Laguerre-type pseudo-spectral scheme for solving transport–fragmentation equations. The method converges rapidly for certain type of fragmentation problems and works under mild restrictions on the growth rate of the coefficients of the equation. Rigorous stability and convergence analyses are provided. Numerical simulations illustrate the performance of the scheme.

Analysis of a Chebyshev-type pseudo-spectral scheme for the nonlinear Schrdinger equation

In this paper, we derive several error estimates that are pertinent to the study of Chebyshev-type spectral approximations on the real line. The results are applied to construct a stable and accurate pseudo-spectral Chebyshev scheme for the nonlinear Schrdinger equation. The new technique has several computational advantages as compared to Fourier and Hermite-type spectral schemes, described in the literature (see e.g., [1][3]. Similar to Hermite-type methods, we do not require domain truncation and/or use of artificial boundary conditions. At the same time, the computational complexity is comparable to the best Fourier-type spectral methods described in the literature.

Asymptotic convergence of cubic Hermite collocation method for parabolic partial differential equation

In this paper, the asymptotic convergence of cubic Hermite collocation method in continuous time for the parabolic partial differential equation is established of order Oh^2. The linear combination of cubic Hermite basis taken as approximating function is evaluated using the zeros of Chebyshev polynomials as collocation points. The theoretical results are verified for two test problems.

Numerical simulation of a transport fragmentation coagulation model

In this paper, we deal with numerical analysis of a transport fragmentation coagulation equation with power fragmentation rates and separable coagulation kernels. For numerical simulations, the model is rewritten in a conservative form and semi-discretized in space using a Laguerre pseudo-spectral method. Some error estimates are derived and efficiency of the numerical scheme is considered. The paper is concluded with several computational examples.

Challenges in the Numerical Solution for Models in Transport Theory

We consider the numerical solution of the linear Boltzmann equation of semiconductor theory in the presence of a weak external field. The numerical algorithm is based on the compressed asymptotic procedure, which provides a general method for the unified treatment of the bulk approximation and the initial layer occurring in conventional perturbation analysis. The numerical experiments are performed in Matlab.

Numerical Solution of BVPs by OCFE using a Hermite Basis

The numerical solution of problems occurring in the simulation process of washing of packed bed of porous particles via the method of orthogonal collocation on finite elements (OCFE) is considered. Essentially, OCFE combines the classical orthogonal collocation method (OCM) and finite element method (FEM). Hermite basis is used in place of Lagrange polynomial basis for the computation.