Spectral analysis on Burgers' equation and its solutions using three different basis functions

DOI10.1007/S40819-018-0525-7zbMath1407.65227OpenAlexW2804580725WikidataQ114218640 ScholiaQ114218640MaRDI QIDQ1794660

Sagithya Thirumalai, Rajeswari Seshadri

Publication date: 15 October 2018

Published in: International Journal of Applied and Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40819-018-0525-7

zbMATH Keywords

Burgers' equationJacobi polynomialsLegendre polynomialsspectral collocation methodChebyshev

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Shock waves and blast waves in fluid mechanics (76L05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Best approximation, Chebyshev systems (41A50) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Approximation by polynomials (41A10)

Related Items (2)

Spectral solutions of system of Volterra integro-differential equations and their error analysis ⋮ A multiple‐relaxation‐time lattice Boltzmann model for Burgers equation

Cites Work

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• A hybrid numerical scheme for the numerical solution of the Burgers' equation
• Lagrange interpolation and modified cubic B-spline differential quadrature methods for solving hyperbolic partial differential equations with Dirichlet and Neumann boundary conditions
• A Haar wavelet quasilinearization approach for numerical simulation of Burgers' equation
• Biorthogonal multiwavelets on the interval for numerical solutions of Burgers' equation
• Numerical solution of nonlinear Burgers' equation using high accuracy multi-quadric quasi-interpolation
• The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves
• A fifth-order finite volume weighted compact scheme for solving one-dimensional Burgers' equation
• A Chebyshev spectral collocation method for solving Burgers'-type equations
• Numerical solution of the Burgers' equation by automatic differentiation
• Global properties of pseudospectral methods
• Spectral collocation methods
• Numerical solution of one-dimensional Burgers equation: Explicit and exact-explicit finite difference methods
• An algorithm based on exponential modified cubic B-spline differential quadrature method for nonlinear Burgers' equation
• A mixed finite difference and boundary element approach to one-dimensional Burgers' equation
• Polynomial based differential quadrature method for numerical solution of nonlinear Burgers equation
• Numerical simulation of two-dimensional sine-Gordon solitons by differential quadrature method
• A numerical scheme based on weighted average differential quadrature method for the numerical solution of Burgers' equation
• A differential quadrature method for numerical solutions of Burgers'‐type equations
• An exact solution for Burger's equation
• Shock wave simulations using Sinc Differential Quadrature Method
• Mixed finite difference and Galerkin methods for solving Burgers equations using interpolating scaling functions
• The partial differential equation u_t + uu_x = μ_xx
• On a quasi-linear parabolic equation occurring in aerodynamics

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