On the numerical solution of nonlinear Burgers'-type equations using meshless method of lines

DOI10.1016/j.amc.2011.11.106zbMath1242.65189OpenAlexW1996577984MaRDI QIDQ422861

Arshad Hussain, Marjan Uddin, Sirajul Haq

Publication date: 18 May 2012

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2011.11.106

zbMATH Keywords

numerical examplesradial basis functionsmethod of linesBurgers' equationmeshless methodsRunge-Kutta method in timeBurgers'-Huxley equationfinite differences in space

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (20)

Unconditionally stable meshless integration of time-domain Maxwell's curl equations ⋮ An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations ⋮ A higher order numerical implicit method for non-linear Burgers' equation ⋮ Efficient numerical techniques for Burgers' equation ⋮ NUMERICAL SOLUTIONS OF SPACE FRACTIONAL VARIABLE-COEFFICIENT KdV–MODIFIED KdV EQUATION BY FOURIER SPECTRAL METHOD ⋮ The analysis of the solution of the <scp>Burgers–Huxley</scp> equation using the Galerkin method ⋮ Numerical solution of Klein-Gordon and sine-Gordon equations by meshless method of lines ⋮ Radial basis functions and level set method for image segmentation using partial differential equation ⋮ A fifth-order finite volume weighted compact scheme for solving one-dimensional Burgers' equation ⋮ Hybrid radial basis function methods of lines for the numerical solution of viscous Burgers' equation ⋮ On the selection of a good value of shape parameter in solving time-dependent partial differential equations using RBF approximation method ⋮ A generalization of the method of lines for the numerical solution of coupled, forced vibration of beams ⋮ RBFs meshless method of lines for time-dependent PDEs with decomposition of interior and boundary data centers ⋮ Nonlinear self-adjointness and generalized conserved quantities of the inviscid Burgers' equation with nonlinear source ⋮ A meshless method for Burgers' equation using MQ-RBF and high-order temporal approximation ⋮ Spectrum-free and meshless solvers of parabolic PDEs ⋮ An efficient Strang splitting technique combined with the multiquadric-radial basis function for the Burgers' equation ⋮ Numerical solutions of generalized Burgers–Fisher and generalized Burgers–Huxley equations using collocation of cubicB-splines ⋮ Unnamed Item ⋮ AN IMPROVED SECOND-ORDER NUMERICAL METHOD FOR THE GENERALIZED BURGERS–FISHER EQUATION

Cites Work

• Unnamed Item
• Unnamed Item
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• Meshless method of lines for the numerical solution of generalized Kuramoto-Sivashinsky equation
• A fourth-order numerical scheme for solving the modified Burgers equation
• Adomian decomposition method for Burgers--Huxley and Burgers--Fisher equations
• A new domain decomposition algorithm for generalized Burgers-Huxley equation based on Chebyshev polynomials and preconditioning
• Spectral collocation method and Darvishi's preconditionings to solve the generalized Burgers-Huxley equation
• A numerical study of the Burgers' equation
• A mesh-free method for the numerical solution of the KdV-Burgers equation
• Numerical solution of complex modified Korteweg-de Vries equation by mesh-free collocation method
• Numerical simulation of the generalized Huxley equation by He's homotopy perturbation method
• Convergence order estimates of meshless collocation methods using radial basis functions
• An efficient numerical scheme for Burger equation
• A finite element approach for solution of Burgers' equation
• Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Transport schemes on a sphere using radial basis functions
• Quartic B-spline collocation method to the numerical solutions of the Burgers' equation
• Solving the generalized Burgers-Huxley equation using the Adomian decomposition method
• B-spline Galerkin methods for numerical solutions of the Burgers' equation
• A numerical solution of the Burgers' equation using septic B-splines
• A numerical solution of the generalized Burgers-Huxley equation by pseudospectral method and Darvishi's preconditioning
• A MATLAB implementation of upwind finite differences and adaptive grids in the method of lines
• Method of lines solutions of the extended Boussinesq equations
• Numerical treatment for the modified Burgers equation
• A meshless method of lines for the numerical solution of KdV equation using radial basis functions
• Solitary wave solutions of the generalised Burgers-Huxley equation
• A Compendium of Partial Differential Equation Models
• Product Approximation for Non-linear Problems in the Finite Element Method
• Exponential convergence andH-c multiquadric collocation method for partial differential equations
• A Collocation Solution For Burgers Equation Using Quadratic B-Spline Finite Elements
• Sonic shocks governed by the modified Burgers' equation
• Numerical solutions of the Burgers–Huxley equation by the IDQ method
• Upwinding in the method of lines

This page was built for publication: On the numerical solution of nonlinear Burgers'-type equations using meshless method of lines