A Highly Accurate Time–Space Pseudospectral Approximation and Stability Analysis of Two Dimensional Brusselator Model for Chemical Systems

Numerical Methods Partial

Balyan

2020

Self Cite

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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

Numerical Methods Partial

Balyan

2020

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“…24 Besides, the pseudospectral method is also an emphatic and alternate numerical scheme for solving a wide range of linear and nonlinear fractional partial differential equations. [25][26][27][28][29][30] Lin and Xu 26 and Mohebbi 31 have used spectral method for the solution and stability analysis of time fractional nonlinear equations. They applied spectral method for space only, and finite difference scheme was used for time.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of time and space fractional coupled Burgers equations using time–space Chebyshev pseudospectral method

Math Methods in App Sciences

Balyan

2020

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The aim of the paper is to develop and analyze a spectrally accurate time–space pseudospectral method to the approximate solution of nonlinear time and space fractional coupled Burgers equations. Liouville–Caputo fractional derivative formula is used to evaluate the fractional derivatives matrix at CGL points. Using the Chebyshev fractional derivative matrices, the given problem is reduced to a system of nonlinear algebraic equations. A mapping is used to transform the nonhomogeneous initial–boundary values to homogeneous initial–boundary values. Error analysis of the proposed method for the equation is presented. A model example of fractional coupled Burgers equations is tested for a set of fractional‐order derivatives. For the proposed method, highly accurate numerical results are obtained, which confirm the accuracy and efficiency of the proposed method.

“…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

Numerical Methods Partial

Shrivastava

Panda

2020

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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.