Chebyshev pseudospectral approximation of two dimensional fractional Schrodinger equation on a convex and rectangular domain

The aim of the paper is to develop and analyze a spectrally accurate pseudospectral method in time and space to find the approximate solution of the viscous Burgers' equation. The method is employed in time and space both at Chebyshev-Gauss-Lobbato (CGL) points. The approximate solution is represented in terms of basis functions. The spectral coefficients are found in such a way that the residual becomes minimum. The given problem is reduced to a system of nonlinear algebraic equations, which is solved by Newton-Raphson's method. Error estimates for interpolating polynomials are derived. The computational experiments are carried out to corroborate the theoretical results and to compare the present method with existing methods in the literature.

“…In

2018

Section: Introductionmentioning

confidence: 99%

A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation

Mittal¹,

Balyan

Sharma

2023

“…There are some authors, who have applied spectral method for numerical solutions of various nonlinear partial differential equations [38–43]. In this paper, we propose a highly accurate Chebyshev pseudospectral method using orthogonal basis functions for numerical solutions of CMKdV equation, in both time and spatial direction.…”

Section: Introductionmentioning

confidence: 99%

“…Equations (4) and (5) represent the interaction of two orthogonal polarized transverse wave, where polarization angle q is defined by tan q = U/V. There are some authors, who have applied spectral method for numerical solutions of various nonlinear partial differential equations [38][39][40][41][42][43]. In this paper, we propose a highly accurate Chebyshev pseudospectral method using orthogonal basis functions for numerical solutions of CMKdV equation, in both time and spatial direction.…”

mentioning

confidence: 99%

Numerical solutions and stability analysis for solitary waves of complex modified Korteweg–de Vries equation using Chebyshev pseudospectral methods

Mittal

Balyan

2020

“…Trofimov and Peskov [40] have also solved the GPE using a conservative finite difference method. Moreover, multidimensional NSE was solved by several other numerical methods, such as riccati expansion method [1], finite difference method [38, 44], finite element method [10] Galerkin finite element method [43], momentum representation method [9], symplectic and multisymplectic methods [2, 39], compact scheme [18], split‐step Fourier scheme [32], compact boundary value method [31], spectral method [3, 28, 29, 30], operational matrix method [23, 27, 37], discrete collocation method based [26], and spline collocation method [22].…”

Section: Introductionmentioning

confidence: 99%

Time–space Jacobi pseudospectral simulation of multidimensional Schrödinger equation

Mittal

Shrivastava

Panda

2020

In this paper, the authors investigate the collision of soliton waves for multidimensional nonlinear Schrödinger equation (NSE) using the time–space Jacobi pseudospectral method. The proposed method is established in both time and space to approximate the solutions and to prove the theory of error estimates and stability analysis for the equations. Using the Jacobi derivatives matrices the given problem is reduced to a system of nonlinear algebraic equations, which will be solved using Newton's Raphson method. For numerical experiments, the method is tested on a number of different examples to study the behavior of collision of two and more than two solitons waves and single soliton wave. Moreover, numerical solutions are demonstrated to justify the theoretical results. The rate of convergence of the proposed method is obtained up to six‐order. The proposed method also preserves mass and energy conservation laws. A comparison of the numerical and exact solutions is depicted in the form of figures and tables.