A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations
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Phumlani G. Dlamini
und
Vusi M. Magagula
Abstract
In this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.
Research funding: None declared.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- ANFIS based system identification of underactuated systems
- The dynamical behavior of mixed type lump solutions on the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation
- A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation
- Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation
- A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations
- Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations
- Integrodifference master equation describing actively growing blood vessels in angiogenesis
- On the behaviors of rough multilinear fractional integral and multi-sublinear fractional maximal operators both on product Lp and weighted Lp spaces
- Approximate controllability of nonlinear Hilfer fractional stochastic differential system with Rosenblatt process and Poisson jumps
- Lie symmetries and singularity analysis for generalized shallow-water equations
- Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system
- Nonlinear wave equation in an inhomogeneous medium from non-standard singular Lagrangians functional with two occurrences of integrals
- Lie symmetry analysis and similarity solutions for the Jimbo – Miwa equation and generalisations
- The barotropic Rossby waves with topography on the earth’s δ-surface
- Synchronization control between discrete uncertain networks with different topologies
- Boundary shape functions methods for solving the nonlinear singularly perturbed problems with Robin boundary conditions
- Global exponential stability analysis of anti-periodic solutions of discontinuous bidirectional associative memory (BAM) neural networks with time-varying delays
- A parallel hybrid implementation of the 2D acoustic wave equation
- Approximate controllability of fractional stochastic evolution equations with nonlocal conditions
- Fractional (3+1)-dim Jimbo Miwa system: invariance properties, exact solutions, solitary pattern solutions and conservation laws
- Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation in an optical fiber
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- ANFIS based system identification of underactuated systems
- The dynamical behavior of mixed type lump solutions on the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation
- A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation
- Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation
- A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations
- Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations
- Integrodifference master equation describing actively growing blood vessels in angiogenesis
- On the behaviors of rough multilinear fractional integral and multi-sublinear fractional maximal operators both on product Lp and weighted Lp spaces
- Approximate controllability of nonlinear Hilfer fractional stochastic differential system with Rosenblatt process and Poisson jumps
- Lie symmetries and singularity analysis for generalized shallow-water equations
- Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system
- Nonlinear wave equation in an inhomogeneous medium from non-standard singular Lagrangians functional with two occurrences of integrals
- Lie symmetry analysis and similarity solutions for the Jimbo – Miwa equation and generalisations
- The barotropic Rossby waves with topography on the earth’s δ-surface
- Synchronization control between discrete uncertain networks with different topologies
- Boundary shape functions methods for solving the nonlinear singularly perturbed problems with Robin boundary conditions
- Global exponential stability analysis of anti-periodic solutions of discontinuous bidirectional associative memory (BAM) neural networks with time-varying delays
- A parallel hybrid implementation of the 2D acoustic wave equation
- Approximate controllability of fractional stochastic evolution equations with nonlocal conditions
- Fractional (3+1)-dim Jimbo Miwa system: invariance properties, exact solutions, solitary pattern solutions and conservation laws
- Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation in an optical fiber
